GEORESOURCES, INC. WARRANT TO PURCHASE SHARES OF COMMON STOCK, PAR VALUE $0.01 PER SHARE

Exhibit 10.34

THE SECURITIES REPRESENTED HEREBY MAY NOT BE TRANSFERRED UNLESS (I) SUCH SECURITIES HAVE BEEN REGISTERED FOR SALE PURSUANT TO THE SECURITIES ACT OF 1933, AS AMENDED, (II) SUCH SECURITIES MAY BE SOLD PURSUANT TO RULE 144 WITHOUT RESTRICTION, OR (III) THE COMPANY HAS RECEIVED AN OPINION OF COUNSEL REASONABLY SATISFACTORY TO IT THAT SUCH TRANSFER MAY LAWFULLY BE MADE WITHOUT REGISTRATION UNDER THE SECURITIES ACT OF 1933 OR QUALIFICATION UNDER APPLICABLE STATE SECURITIES LAWS. NOTWITHSTANDING THE FOREGOING, THE SECURITIES MAY BE PLEDGED IN CONNECTION WITH A BONA FIDE MARGIN ACCOUNT OR OTHER LOAN OR FINANCING ARRANGEMENT SECURED BY THE SECURITIES PROVIDED THAT SUCH PLEDGE DOES NOT CONSTITUTE OR RESULT IN A TRANSFER OF THE SECURITIES UNDER ANY APPLICABLE LAWS, RULES OR REGULATIONS.

No.                    

GEORESOURCES, INC.

WARRANT TO PURCHASE              SHARES OF

COMMON STOCK, PAR VALUE $0.01 PER SHARE

For VALUE RECEIVED,              (“Warrantholder”), is entitled to purchase, subject to the provisions of this Warrant, from GEORESOURCES, INC., a Colorado corporation (“Company”), at any time not earlier than the date that is six months after the date hereof (the “Initial Exercise Date”) and not later than 5:00 P.M., Eastern time, on June 9, 2013 (the “Expiration Date”), at an exercise price per share equal to $32.43 (the “Exercise Price”),              shares (“Warrant Shares”) of the Company’s Common Stock, par value $0.01 per share (“Common Stock”). The number of Warrant Shares purchasable upon exercise of this Warrant and the Exercise Price shall be subject to adjustment from time to time as described herein.

Section 1. Registration. The Company shall maintain books for the transfer and registration of this Warrant. Upon the initial issuance of this Warrant, the Company shall issue and register this Warrant in the name of the Warrantholder.

Section 2. Transfers. As provided herein, this Warrant may be transferred only pursuant to a registration statement filed under the Securities Act of 1933, as amended (the “Securities Act”), or an exemption from such registration. Subject to such restrictions, the Company shall transfer this Warrant from time to time upon the books to be maintained by the Company for that purpose, upon surrender thereof for transfer, properly endorsed or accompanied by appropriate instructions for transfer and such other documents as may be reasonably required by the Company, including, if required by the Company, an opinion of its counsel to the effect that such transfer is exempt from the registration requirements of the Securities Act, to establish that such transfer is being made in accordance with the terms hereof, and a new Warrant shall be issued to the transferee and the surrendered Warrant shall be canceled by the Company.

Section 3. Exercise of Warrant.

(a) This Warrant may be exercised in whole or in part at any time on or after the Initial Exercise Date and prior to the Expiration Date upon delivery of the notice of exercise form attached hereto as Appendix A (the “Notice of Exercise”) and payment by cash, certified check or wire transfer (or, in certain circumstances, by cashless exercise as provided in Section 3(d)) for the aggregate Exercise Price for that number of Warrant Shares then being purchased, to the Company during normal business hours on any day other than a Saturday or Sunday on which banks are open for business in New York City (a “Business Day”) at the Company’s principal executive offices (or such other office or agency of the Company as the Company may designate by notice to the Warrantholder). The Warrant Shares so purchased shall be deemed to be issued to the Warrantholder or the Warrantholder’s designee, as the record owner of such shares, as of 5:00 P.M. New York City time on the date on which the aggregate Exercise Price shall have been paid and the completed Notice of Exercise shall have been delivered. Certificates for the Warrant Shares so purchased, representing the aggregate number of shares specified in the Notice of Exercise, shall be transmitted by the Company’s transfer agent by crediting the account of the Warrantholder’s prime broker with The Depository Trust Company (“DTC”) through its Deposit / Withdrawal At Custodian (“DWAC”) system if the Company is a participant in such system, and otherwise by physical delivery to the address specified by the Warrantholder in the Notice of Exercise, within a reasonable time, not exceeding three (3) Trading Days (as defined below) after this Warrant shall have been so exercised, including payment of the aggregate Exercise Price and the delivery of a completed Notice of Exercise (the “Warrant Share Delivery Date”). The certificates so delivered shall be in such denominations as may be requested by the Warrantholder and shall be registered in the name of the Warrantholder or such other name as shall be designated by the Warrantholder in the Notice of Exercise. In addition to any other rights available to the Warrantholder, if the Company fails to deliver to the Warrantholder a certificate or certificates representing the Warrant Shares pursuant to an exercise on or before this Warrant Share Delivery Date, and if after such date the Warrantholder is required by its broker to purchase (in an open market transaction or otherwise) shares of Common Stock to deliver in satisfaction of a sale by the Warrantholder of the Warrant Shares which the Warrantholder anticipated receiving upon such exercise (a “Buy-In”), then the Company shall either (i) pay cash to the Warrantholder in an amount equal to the Warrantholder ‘s total purchase price (including brokerage commissions, if any) for the shares of Common Stock so purchased (the “Buy-In Price”), at which point the Company’s obligation to deliver such certificate (and to issue such shares of Common Stock) or credit such Holder’s balance account with DTC shall terminate, or (ii) promptly honor its obligation to deliver to the Warrantholder a certificate or certificates representing such shares of Common Stock or credit such Warrantholder’s balance account with DTC and pay cash to the Warrantholder in an amount equal to the excess (if any) of the Buy-In Price over the product of (A) such number of shares of Common Stock, times (B) the Closing Bid Price on the date of exercise. Warrantholder shall provide the Company written notice indicating the amounts payable to the Warrantholder in respect to the Buy-In, together with applicable confirmations and other evidence reasonably requested by the Company. Nothing herein shall limit a Warrantholder’s right to pursue any other remedies available to it hereunder, at law or in equity including, without limitation, a decree of specific performance and/or injunctive relief with respect to the Company’s failure to timely deliver certificates representing shares of Common Stock upon exercise of this Warrant as required pursuant to the terms hereof. Notwithstanding anything herein to the contrary, the Warrantholder shall not be required to physically surrender this Warrant to the Company until

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the Warrantholder has purchased all of the Warrant Shares available hereunder and this Warrant has been exercised in full, in which case, the Warrantholder shall surrender this Warrant to the Company for cancellation within three (3) Trading Days of the date the final Notice of Exercise is delivered to the Company. Partial exercises of this Warrant resulting in purchases of a portion of the total number of Warrant Shares available hereunder shall have the effect of lowering the outstanding number of Warrant Shares purchasable hereunder in an amount equal to the applicable number of Warrant Shares purchased. The Warrantholder and the Company shall maintain records showing the number of Warrant Shares purchased and the date of such purchases. The Company shall deliver any objection to any Notice of Exercise Form within one Business Day of receipt of such notice. In the event of any dispute or discrepancy, the records of the Company’s transfer agent shall be controlling and determinative in the absence of manifest error. The Warrantholder and any assignee, by acceptance of this Warrant, acknowledge and agree that, by reason of the provisions of this paragraph, following the purchase of a portion of the Warrant Shares hereunder, the number of Warrant Shares available for purchase hereunder at any given time may be less than the amount stated on the face hereof. For purposes of this Warrant (i) a “Trading Day” means (A) a day on which the Common Stock is traded on a Trading Market (as defined below), or (B) if the Common Stock is not listed on a Trading Market, a day on which the Common Stock is traded on the over the counter market, as reported by the National Association of Securities Dealers, Inc. OTC Bulletin Board (the “Bulletin Board”), or (C) if the Common Stock is not quoted on the Bulletin Board, a day on which prices for the Common Stock are reported in the Pink Sheets published by Pink Sheets LLC (or any similar organization or agency succeeding to its functions of reporting prices); provided, that in the event that the Common Stock is not listed, quoted or reported as set forth in (A), (B) and (C) hereof, then Trading Day shall mean a Business Day and (ii) “Trading Market” means the following markets or exchanges on which the Common Stock is listed or quoted for trading on the date in question: the NASDAQ Global Select Market, the NASDAQ Global Market, The NASDAQ Capital Market, the American Stock Exchange or the New York Stock Exchange.

In addition to any other rights available to the Warrantholder, if the Company fails to deliver to the Warrantholder a certificate or certificates representing the Warrant Shares pursuant to an exercise on or before the Warrant Share Delivery Date, the Company shall be liable to the Warrantholder for liquidated damages in an amount equal to 1.5% of the aggregate Exercise Price of the Warrant Shares issuable pursuant to such exercise for each thirty (30) day period (or pro rata for any portion thereof) beyond the Warrant Share Delivery Date.

(b) If this Warrant shall have been exercised in part, the Company shall, at its own expense and at the time of delivery of the certificate or certificates representing Warrant Shares, deliver to the Warrantholder a new Warrant evidencing the rights of the Warrantholder to purchase the unpurchased Warrant Shares called for by this Warrant, which new Warrant shall in all other respects be identical to this Warrant.

(c) Notwithstanding anything to the contrary herein, the Warrantholder shall not have the right to exercise any portion of this Warrant, pursuant to Section 3 or otherwise, to the extent that after giving effect to such issuance after exercise, the Warrantholder (together with the Warrantholder’s affiliates), as set forth on the applicable Notice of Exercise, would beneficially own in excess of 4.99% of the number of shares of the Common Stock outstanding immediately after giving effect to such issuance. For purposes of the foregoing sentence, the

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number of shares of Common Stock beneficially owned by the Warrantholder and its affiliates shall include the number of shares of Common Stock issuable upon exercise of this Warrant with respect to which the determination of such sentence is being made, but shall exclude the number of shares of Common Stock which would be issuable upon (A) exercise of the remaining, nonexercised portion of this Warrant beneficially owned by the Warrantholder or any of its affiliates and (B) exercise or conversion of the unexercised or nonconverted portion of any other securities of the Company (including, without limitation, any other shares of Common Stock or Warrants) subject to a limitation on conversion or exercise analogous to the limitation contained herein beneficially owned by the Warrantholder or any of its affiliates. Except as set forth in the preceding sentence, for purposes of this Section 3(c), beneficial ownership shall be calculated in accordance with Section 13(d) of the Exchange Act, it being acknowledged by the Warrantholder that the Company is not representing to the Warrantholder that such calculation is in compliance with Section 13(d) of the Exchange Act and the Warrantholder is solely responsible for any schedules required to be filed in accordance therewith. For purposes of this Section 3(c), in determining the number of outstanding shares of Common Stock, the Warrantholder may rely on the number of outstanding shares of Common Stock as reflected in the latest of (x) the Company’s most recent Form 10-Q or Form 10-K, as the case may be, (y) a more recent public announcement by the Company or (z) any other notice by the Company or the Company’s transfer agent setting forth the number of shares of Common Stock outstanding. Following the written or oral request of the Warrantholder, the Company shall, or shall cause its transfer agent to, within two Trading Days confirm orally and in writing to the Warrantholder the number of shares of Common Stock then outstanding. In any case, the number of outstanding shares of Common Stock shall be determined after giving effect to the conversion or exercise of securities of the Company, including this Warrant, by the Warrantholder or its Affiliates since the date as of which such number of outstanding shares of Common Stock was reported. The provisions of this Section 3(c) may be waived by the Warrantholder, at the election of the Warrantholder, upon not less than 61 days’ prior notice to the Company, and the provisions of this Section 3(c) shall continue to apply until such 61st day (or such later date, as determined by the Warrantholder, as may be specified in such notice of waiver).

(d) Notwithstanding any other provision contained herein to the contrary, so long as the Company is required under the Registration Rights Agreement dated as of June 5, 2008 among the Company and the investors party thereto (the “Registration Rights Agreement”) to have effected the registration of the Warrant Shares for sale to the public pursuant to a Registration Statement (as such term is defined in the Registration Rights Agreement), if the Warrant Shares may not be freely sold to the public for any reason (including, but not limited to, the failure of the Company to have effected the registration of the Warrant Shares, the failure to have a current prospectus available for delivery or otherwise, or during the period of any Allowable Grace Period (as defined in the Registration Rights Agreement)), the Warrantholder may elect to receive, without the payment by the Warrantholder of the aggregate Exercise Price in respect of the shares of Common Stock to be acquired, shares of Common Stock equal to the value of this Warrant or any portion hereof by the surrender of this Warrant (or such portion of this Warrant being so exercised) together with the Net Issue Election Notice annexed hereto as Appendix B duly executed, at the office of the Company. Thereupon, the Company shall issue to the Warrantholder such number of fully paid, validly issued and nonassessable shares of Common Stock as is computed using the following formula:

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X = Y (A - B)

A

where

X = the number of shares of Common Stock which the Warrantholder has then requested be issued to the Warrantholder;

Y = the number of Warrant Shares covered by this Warrant that the Warrantholder is surrendering at such time for cashless exercise (including both shares to be issued to the Warrantholder and shares to be canceled as payment therefor);

A = the Market Price (as defined below) of one share of Common Stock as at the time the net issue election is made; and

B = the Exercise Price in effect under this Warrant at the time the net issue election is made.

Section 4. Compliance with the Securities Act of 1933. If the Registration Statement is not effective at any time that this Warrant is exercised, (i) the Warrant Shares issued upon such exercise shall be “restricted securities,” (ii) the stock certificate evidencing the Warrant Shares shall bear a restrictive legend set forth on the first page of this Warrant unless counsel to the Company is of the opinion that such legend is not necessary. In addition, as a condition precedent to issuance of the Warrant Shares upon such exercise, the Warrantholder shall be required to execute an investment representation statement in the form provided by the Company as evidence of the Warrantholder’s qualifications to purchase Common Stock in a “private placement” that is exempt from registration pursuant to Section 4(2) of the Securities Act.

Section 5. Payment of Taxes. The Company will pay any documentary stamp taxes attributable to the initial issuance of Warrant Shares issuable upon the exercise of this Warrant; provided, however, that the Company shall not be required to pay any tax or taxes which may be payable in respect of any transfer involved in the issuance or delivery of any certificates for Warrant Shares in a name other than that of the Warrantholder in respect of which such shares are issued, and in such case, the Company shall not be required to issue or deliver any certificate for Warrant Shares or any Warrant until the person requesting the same has paid to the Company the amount of such tax or has established to the Company’s reasonable satisfaction that such tax has been paid. The Warrantholder shall be responsible for income taxes due under federal, state or other law, if any such tax is due.

Section 6. Mutilated or Missing Warrants. In case this Warrant shall be mutilated, lost, stolen, or destroyed, the Company shall issue in exchange and substitution of and upon cancellation of the mutilated Warrant, or in lieu of and substitution for this Warrant lost, stolen or destroyed, a new Warrant of like tenor and for the purchase of a like number of Warrant Shares, but only upon receipt of evidence reasonably satisfactory to the Company of such loss, theft or destruction of this Warrant, and with respect to a lost, stolen or destroyed Warrant, reasonable indemnity or bond with respect thereto, if requested by the Company.

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Section 7. Reservation of Common Stock. The Company hereby represents and warrants that there have been reserved, and the Company shall at all applicable times keep reserved until issued (if necessary) as contemplated by this Section 7, out of the authorized and unissued shares of Common Stock, sufficient shares to provide for the exercise of the rights of purchase represented by this Warrant. The Company agrees that all Warrant Shares issued upon due exercise of this Warrant shall be, at the time of delivery of the certificates for such Warrant Shares, duly authorized, validly issued, fully paid and non-assessable shares of Common Stock of the Company.

Section 8. Adjustments. The Exercise Price and number of Warrant Shares subject to this Warrant shall be subject to adjustment from time to time as set forth in this Section 8.

(a) If the Company shall, at any time or from time to time while this Warrant is outstanding, pay a dividend or make a distribution on its Common Stock in shares of Common Stock, subdivide its outstanding shares of Common Stock into a greater number of shares or combine its outstanding shares of Common Stock into a smaller number of shares or issue by reclassification of its outstanding shares of Common Stock any shares of its capital stock (including any such reclassification in connection with a consolidation or merger in which the Company is the continuing corporation), then the number of Warrant Shares purchasable upon exercise of this Warrant and the Exercise Price in effect immediately prior to the date upon which such change shall become effective, shall be adjusted by the Company so that the Warrantholder thereafter exercising this Warrant shall be entitled to receive the number of shares of Common Stock or other capital stock which the Warrantholder would have received if this Warrant had been exercised immediately prior to such event upon payment of an Exercise Price that has been adjusted to reflect a fair allocation of the economics of such event to the Warrantholder. Such adjustments shall be made successively whenever any event listed above shall occur.

(b) If any capital reorganization, reclassification of the capital stock of the Company, consolidation or merger of the Company with another corporation in which the Company is not the survivor, or sale, transfer or other disposition of all or substantially all of the Company’s assets to another corporation shall be effected (each, a “Fundamental Transaction”), then, as a condition of such Fundamental Transaction, lawful and adequate provision shall be made whereby each Warrantholder shall thereafter have the right to exercise this Warrant and receive upon the basis and upon the terms and conditions herein specified and in lieu of the Warrant Shares immediately theretofore issuable upon exercise of this Warrant, such shares of stock, securities or assets as would have been issuable or payable with respect to or in exchange for a number of Warrant Shares equal to the number of Warrant Shares immediately theretofore issuable upon exercise of this Warrant, had this Warrant been exercised in full immediately prior to such Fundamental Transaction (the “Transaction Consideration”), and in any such case appropriate provision (as determined in good faith by the Board of Directors of the Company) shall be made with respect to the rights and interests of each Warrantholder to the end that the provisions hereof (including, without limitation, provision for adjustment of the Exercise Price) shall thereafter be applicable, as nearly equivalent as may be practicable in relation to any Transaction Consideration deliverable upon the exercise hereof. The Company shall not effect any such Fundamental Transaction unless prior to or simultaneously with the consummation thereof the successor corporation or entity (if other than the Company) resulting from such

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consolidation or merger, or the corporation or entity purchasing or otherwise acquiring such assets or other appropriate corporation or entity shall assume the obligation to deliver to the Warrantholder, at the last address of the Warrantholder appearing on the books of the Company, such Transaction Consideration as, in accordance with the foregoing provisions, the Warrantholder may be entitled to receive upon exercise hereof, and the other obligations under this Warrant. Without limiting the generality of the foregoing, the terms of any agreement pursuant to which a Fundamental Transaction is effected shall include terms requiring any such successor or surviving entity to comply with the provisions of this Section 8(b) and insuring that this Warrant (or any such replacement security) will be similarly adjusted upon any subsequent transaction analogous to a Fundamental Transaction. The aggregate Exercise Price for this Warrant will not be affected by any such Fundamental Transaction, but the Company shall apportion such aggregate Exercise Price among the Transaction Consideration in a reasonable manner reflecting the relative value of any different components of the Transaction Consideration, if applicable. If holders of Common Stock are given any choice as to the securities, cash or property to be received in a Fundamental Transaction, then the Warrantholder shall be given the same choice as to the Transaction Consideration it receives upon any exercise of this Warrant following such Fundamental Transaction. At the Warrantholder’s request, any successor to the Company or surviving entity in such Fundamental Transaction shall issue to the Warrantholder a new Warrant consistent with the foregoing provisions and evidencing the Warrantholder’s right to purchase the Transaction Consideration for the aggregate Exercise Price upon exercise thereof. Notwithstanding the foregoing provisions of this Section 8(b), in the event of a Fundamental Transaction, other than a Fundamental Transaction in which the successor corporation is a publicly traded corporation whose common stock is quoted or listed for trading on a Trading Market assumes this Warrant such that this Warrant or any warrant issued in substitution herefor shall be exercisable for the publicly traded common stock of such successor corporation, then the Company or any successor entity shall pay at the Warrantholder’s option, exercisable at any time concurrently with or within 30 days after the consummation of the Fundamental Transaction, an amount of cash equal to the value of this Warrant as determined in accordance with the Black Scholes Option Pricing Model obtained from the “OV” function on Bloomberg L.P. using (i) a price per share of Common Stock equal to the VWAP (as defined below) of the Common Stock for the Trading Day immediately preceding the date of consummation of the applicable Fundamental Transaction, (ii) a risk-free interest rate corresponding to the U.S. Treasury rate for a period equal to the remaining term of this Warrant as of the date of consummation of the applicable Fundamental Transaction and (iii) an expected volatility equal to the 100 day volatility obtained from the “HVT” function on Bloomberg L.P. determined as of the Trading Day immediately following the public announcement of the applicable Fundamental Transaction. The provisions of this Section 8(b) shall similarly apply to successive Fundamental Transactions. For purposes of this Warrant “VWAP” means for any date, the price determined by the first of the following clauses that applies: (a) if the Common Stock is then listed or quoted on a Trading Market, the volume weighted average of the prices per share of the Common Stock traded on such date (or the nearest preceding date) on the Trading Market on which the Common Stock is then listed or quoted as reported by Bloomberg L.P. (based on a Trading Day from 9:30 A.M. New York City time to 4:00 P.M. New York City time); (b) if the Common Stock is not then listed or quoted on a Trading Market and if prices for the Common Stock are then quoted on the Bulletin Board, the volume weighted average of the prices per share of the Common Stock traded on such date (or the nearest preceding date) on the

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Bulletin Board; (c) if the Common Stock is not then listed or quoted on the Bulletin Board and if prices for the Common Stock are then reported in the Pink Sheets published by Pink Sheets LLC (or a similar organization or agency succeeding to its functions of reporting prices), the last bid price per share of the Common Stock so reported on such date (or the most recent bid price if none is reported for such date); or (d) in all other cases, the fair market value of a share of Common Stock as determined by an independent appraiser selected in good faith by the Board of Directors of the Company.

(c) In case the Company shall fix a payment date for the making of a distribution to all holders of Common Stock (including any such distribution made in connection with a consolidation or merger in which the Company is the continuing corporation) of evidences of indebtedness or assets (other than cash dividends or cash distributions payable out of consolidated earnings or earned surplus or dividends or distributions referred to in Section 8(a)), or subscription rights or warrants, the Exercise Price to be in effect after such payment date shall be determined by multiplying the Exercise Price in effect immediately prior to such payment date by a fraction, the numerator of which shall be the total number of shares of Common Stock outstanding multiplied by the Market Price (as defined below) per share of Common Stock immediately prior to such payment date, less the fair market value (as determined by the Company’s Board of Directors in good faith) of said assets or evidences of indebtedness so distributed, or of such subscription rights or warrants, and the denominator of which shall be the total number of shares of Common Stock outstanding multiplied by such Market Price per share of Common Stock immediately prior to such payment date. “Market Price” as of a particular date (the “Valuation Date”) shall mean the following: (i) if the Common Stock is then listed on a national stock exchange, the closing sale price of one share of Common Stock on such exchange on the last trading day prior to the Valuation Date; (ii) if the Common Stock is then quoted on The Nasdaq Stock Market, Inc. (“Nasdaq”), the Bulletin Board or such similar exchange or association, the closing sale price of one share of Common Stock on Nasdaq, the Bulletin Board or such other exchange or association on the last trading day prior to the Valuation Date or, if no such closing sale price is available, the average of the high bid and the low asked price quoted thereon on the last trading day prior to the Valuation Date; or (iii) if the Common Stock is not then listed on a national stock exchange or quoted on Nasdaq, the Bulletin Board or such other exchange or association, the fair market value of one share of Common Stock as of the Valuation Date, shall be determined in good faith by the Board of Directors of the Company and the Warrantholder. If the Common Stock is not then listed on a national securities exchange or quoted on Nasdaq, the Bulletin Board or such other exchange or association, the Board of Directors of the Company shall respond promptly, in writing, to an inquiry by the Warrantholder prior to the exercise hereunder as to the fair market value of a share of Common Stock as determined by the Board of Directors of the Company. In the event that the Board of Directors of the Company and the Warrantholder are unable to agree upon the fair market value in respect of this Section 8(c), the Company and the Warrantholder shall jointly select an appraiser, who is experienced in such matters. The decision of such appraiser shall be final and conclusive, and the cost of such appraiser shall be borne equally by the Company and the Warrantholder. Such adjustment shall be made successively whenever such a payment date is fixed.

(d) An adjustment to the Exercise Price shall become effective immediately after the payment date in the case of each dividend or distribution and immediately after the effective date of each other event which requires an adjustment.

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(e) In the event that, as a result of an adjustment made pursuant to this Section 8, the Warrantholder shall become entitled to receive any shares of capital stock of the Company other than shares of Common Stock, the number of such other shares so receivable upon exercise of this Warrant shall be subject thereafter to adjustment from time to time in a manner and on terms as nearly equivalent as practicable to the provisions with respect to the Warrant Shares contained in this Warrant.

(f) Except as provided in Section 8(g), if and whenever the Company shall issue or sell, or is, in accordance with any of Sections 8(f)(1) - (7), deemed to have issued or sold, any shares of Common Stock for no consideration or for a consideration per share less than the Exercise Price in effect immediately prior to the time of such issue or sale, then and in each such case (a “Trigger Issuance”) the then-existing Exercise Price, shall be reduced, as of the close of business on the effective date of the Trigger Issuance, to a price determined as follows:

where

“A” equals the number of shares of Common Stock outstanding, including Additional Shares of Common Stock (as defined below) deemed to be issued hereunder, immediately preceding such Trigger Issuance;

“B” equals the Exercise Price in effect immediately preceding such Trigger Issuance;

“C” equals the number of Additional Shares of Common Stock issued or deemed issued hereunder as a result of the Trigger Issuance; and

“D” equals the aggregate consideration, if any, received or deemed to be received by the Company upon such Trigger Issuance;

provided, however, that in no event shall the Exercise Price after giving effect to such Trigger Issuance be greater than the Exercise Price in effect prior to such Trigger Issuance.

For purposes of this Section 8(f), “Additional Shares of Common Stock” shall mean all shares of Common Stock issued by the Company or deemed to be issued pursuant to this Section 8(f), other than Excluded Issuances (as defined in Section 8(g)).

For purposes of this Section 8(f), the following Sections 8(f)(1) - (f)(7) shall also be applicable:

(1) Issuance of Rights or Options. In case at any time the Company shall in any manner grant (directly and not by assumption in a merger or otherwise) any warrants or other rights to subscribe for or to purchase, or any options for the purchase of, Common Stock or any stock or security convertible into or exchangeable for Common Stock (such warrants, rights or options being called “Options” and such convertible or exchangeable stock or securities being called “Convertible Securities”) whether or not such Options or the right to convert or

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exchange any such Convertible Securities are immediately exercisable, and the price per share for which Common Stock is issuable upon the exercise of such Options or upon the conversion or exchange of such Convertible Securities (determined by dividing (i) the sum (which sum shall constitute the applicable consideration) of (x) the total amount, if any, received or receivable by the Company as consideration for the granting of such Options, plus (y) the aggregate amount of additional consideration payable to the Company upon the exercise of all such Options, plus (z), in the case of such Options which relate to Convertible Securities, the aggregate amount of additional consideration, if any, payable upon the issue or sale of such Convertible Securities and upon the conversion or exchange thereof, by (ii) the total maximum number of shares of Common Stock issuable upon the exercise of such Options or upon the conversion or exchange of all such Convertible Securities issuable upon the exercise of such Options) shall be less than the Exercise Price in effect immediately prior to the time of the granting of such Options, then the total number of shares of Common Stock issuable upon the exercise of such Options or upon conversion or exchange of the total amount of such Convertible Securities issuable upon the exercise of such Options shall be deemed to have been issued for such price per share as of the date of granting of such Options or the issuance of such Convertible Securities and thereafter shall be deemed to be outstanding for purposes of adjusting the Exercise Price. Except as otherwise provided in Section 8(f)(3), no adjustment of the Exercise Price shall be made upon the actual issue of such Common Stock or of such Convertible Securities upon exercise of such Options or upon the actual issue of such Common Stock upon conversion or exchange of such Convertible Securities.

(2) Issuance of Convertible Securities. In case the Company shall in any manner issue (directly and not by assumption in a merger or otherwise) or sell any Convertible Securities, whether or not the rights to exchange or convert any such Convertible Securities are immediately exercisable, and the price per share for which Common Stock is issuable upon such conversion or exchange (determined by dividing (i) the sum (which sum shall constitute the applicable consideration) of (x) the total amount received or receivable by the Company as consideration for the issue or sale of such Convertible Securities, plus (y) the aggregate amount of additional consideration, if any, payable to the Company upon the conversion or exchange thereof, by (ii) the total number of shares of Common Stock issuable upon the conversion or exchange of all such Convertible Securities) shall be less than the Exercise Price in effect immediately prior to the time of such issue or sale, then the total maximum number of shares of Common Stock issuable upon conversion or exchange of all such Convertible Securities shall be deemed to have been issued for such price per share as of the date of the issue or sale of such Convertible Securities and thereafter shall be deemed to be outstanding for purposes of adjusting the Exercise Price, provided that (a) except as otherwise provided in Section 8(f)(3), no adjustment of the Exercise Price shall be made upon the actual issuance of such Common Stock upon conversion or exchange of such Convertible Securities and (b) no further adjustment of the Exercise Price shall be made by reason of the issue or sale of Convertible Securities upon

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exercise of any Options to purchase any such Convertible Securities for which adjustments of the Exercise Price have been made pursuant to the other provisions of Section 8(f).

(3) Change in Option Price or Conversion Rate. Upon the happening of any of the following events, namely, if the purchase price provided for in any Option referred to in Section 8(f)(l), the additional consideration, if any, payable upon the conversion or exchange of any Convertible Securities referred to in Section 8(f)(1) or Section 8(f)(2), or the rate at which Convertible Securities referred to in Section 8(f)(1) or Section 8(f)(2) are convertible into or exchangeable for Common Stock shall change at any time (including, but not limited to, changes under or by reason of provisions designed to protect against dilution), the Exercise Price in effect at the time of such event shall forthwith be readjusted to the Exercise Price which would have been in effect at such time had such Options or Convertible Securities still outstanding provided for such changed purchase price, additional consideration or conversion rate, as the case may be, at the time initially granted, issued or sold. On the termination of any Option for which any adjustment was made pursuant to this Section 8(f) or any right to convert or exchange Convertible Securities for which any adjustment was made pursuant to this Section 8(f) (including without limitation upon the redemption or purchase for consideration of such Convertible Securities by the Company), the Exercise Price then in effect hereunder shall forthwith be changed to the Exercise Price which would have been in effect at the time of such termination had such Option or Convertible Securities, to the extent outstanding immediately prior to such termination, never been issued.

(4) Stock Dividends. Subject to the provisions of this Section 8(f), in case the Company shall declare a dividend or make any other distribution upon any stock of the Company (other than the Common Stock) payable in Common Stock, Options or Convertible Securities, then any Common Stock, Options or Convertible Securities, as the case may be, issuable in payment of such dividend or distribution shall be deemed to have been issued or sold without consideration.

(5) Consideration for Stock. In case any shares of Common Stock, Options or Convertible Securities shall be issued or sold for cash, the consideration received therefor shall be deemed to be the net amount received by the Company therefor, after deduction therefrom of any expenses incurred or any underwriting commissions or concessions paid or allowed by the Company in connection therewith. In case any shares of Common Stock, Options or Convertible Securities shall be issued or sold for a consideration other than cash, the amount of the consideration other than cash received by the Company shall be deemed to be the fair value of such consideration as determined in good faith by the Board of Directors of the Company, after deduction of any expenses incurred or any underwriting commissions or concessions paid or allowed by the Company in connection therewith. In case any Options shall be issued in connection with the issue and sale of other securities of the Company, together comprising one integral transaction in which no specific consideration is allocated to such Options

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by the parties thereto, such Options shall be deemed to have been issued for such consideration as determined in good faith by the Board of Directors of the Company. If Common Stock, Options or Convertible Securities shall be issued or sold by the Company and, in connection therewith, other Options or Convertible Securities (the “Additional Rights”) are issued, then the consideration received or deemed to be received by the Company shall be reduced by the fair market value of the Additional Rights (as determined using the Black-Scholes Option Pricing Model or another method mutually agreed to by the Company and the Warrantholder). The Board of Directors of the Company shall respond promptly, in writing, to an inquiry by the Warrantholder as to the fair market value of the Additional Rights. In the event that the Board of Directors of the Company and the Warrantholder are unable to agree upon the fair market value of the Additional Rights, the Company and the Warrantholder shall jointly select an appraiser, who is experienced in such matters. The decision of such appraiser shall be final and conclusive, and the cost of such appraiser shall be borne evenly by the Company and the Warrantholder.

(6) Record Date. In case the Company shall take a record of the holders of its Common Stock for the purpose of entitling them (i) to receive a dividend or other distribution payable in Common Stock, Options or Convertible Securities or (ii) to subscribe for or purchase Common Stock, Options or Convertible Securities, then such record date shall be deemed to be the date of the issue or sale of the shares of Common Stock deemed to have been issued or sold upon the declaration of such dividend or the making of such other distribution or the date of the granting of such right of subscription or purchase, as the case may be.

(7) Treasury Shares. The number of shares of Common Stock outstanding at any given time shall not include shares owned or held by or for the account of the Company or any of its wholly-owned subsidiaries, and the disposition of any such shares (other than the cancellation or retirement thereof) shall be considered an issue or sale of Common Stock for the purpose of this Section 8(f).

(8) Nasdaq Limitation. Notwithstanding any other provision in Section 8(f) to the contrary, if a reduction in the Exercise Price pursuant to Section 8(f) (other than as set forth in this Section 8(f)(8)) would require the Company to obtain stockholder approval of the transactions contemplated by the Purchase Agreement pursuant to Nasdaq Marketplace Rule 4350(i) and such stockholder approval has not been obtained, (i) the Exercise Price shall be reduced to the maximum extent that would not require stockholder approval under such Rule, and (ii) the Company shall use its commercially reasonable efforts to obtain such stockholder approval as soon as reasonably practicable, including by calling a special meeting of stockholders to vote on such Exercise Price adjustment.

(g) Anything herein to the contrary notwithstanding, the Company shall not be required to make any adjustment of the Exercise Price in the case of the issuance of (A) capital stock, Options or Convertible Securities issued to directors, officers, employees or consultants of the Company in connection with their service as directors of the Company, their

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employment by the Company or their retention as consultants by the Company pursuant to an equity compensation program approved by the Board of Directors of the Company or the compensation committee of the Board of Directors of the Company, (B) shares of Common Stock issued upon the conversion or exercise of Options or Convertible Securities issued prior to the date hereof; provided that neither the conversion price or exercise price nor number of shares issuable under such Options or Convertible Securities is amended, modified or changed after the date hereto other than pursuant to the provisions of such Options or Convertible Securities as they exist as of the date hereof, (C) securities issued pursuant to that certain Purchase Agreement dated June 5, 2008, among the Company and the Investors named therein (the “Purchase Agreement”) and securities issued upon the exercise or conversion of those securities, and (D) shares of Common Stock issued or issuable by reason of a dividend, stock split or other distribution on shares of Common Stock (but only to the extent that such a dividend, split or distribution results in an adjustment in the Exercise Price pursuant to the other provisions of this Warrant) (collectively, “Excluded Issuances”).

(h) Upon any adjustment to the Exercise Price pursuant to Section 8(f), the number of Warrant Shares purchasable hereunder shall be adjusted by multiplying such number by a fraction, the numerator of which shall be the Exercise Price in effect immediately prior to such adjustment and the denominator of which shall be the Exercise Price in effect immediately thereafter. Notwithstanding any other provisions of Section 8(f) to the contrary, no adjustment provided for in Section 8(f) shall result in a reduction of the Exercise Price to an amount less than $32.43 per Warrant Share (as appropriately adjusted for the occurrence of any events listed in Sections 8(a), 8(b) or 8(c)).

Section 9. Fractional Interest. The Company shall not be required to issue fractions of Warrant Shares upon the exercise of this Warrant. If any fractional share of Common Stock would, except for the provisions of the first sentence of this Section 9, be deliverable upon such exercise, the Company, in lieu of delivering such fractional share, shall pay to the exercising Warrantholder an amount in cash equal to the Market Price of such fractional share of Common Stock on the date of exercise.

Section 10. Benefits. Nothing in this Warrant shall be construed to give any person, firm or corporation (other than the Company and the Warrantholder) any legal or equitable right, remedy or claim, it being agreed that this Warrant shall be for the sole and exclusive benefit of the Company and the Warrantholder.

Section 11. Notices to Warrantholder. Upon the happening of any event requiring an adjustment of the Exercise Price, the Company shall promptly give written notice thereof to the Warrantholder at the address appearing in the records of the Company, stating the adjusted Exercise Price and the adjusted number of Warrant Shares resulting from such event and setting forth in reasonable detail the method of calculation and the facts upon which such calculation is based. Failure to give such notice to the Warrantholder or any defect therein shall not affect the legality or validity of the subject adjustment.

Section 12. Identity of Transfer Agent. The Transfer Agent for the Common Stock is Wells Fargo Shareowner Services. Upon the appointment of any subsequent transfer agent for the Common Stock or other shares of the Company’s capital stock issuable upon the exercise of the rights of purchase represented by this Warrant, the Company will mail to the Warrantholder a statement setting forth the name and address of such transfer agent.

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Section 13. Notices. Unless otherwise provided, any notice required or permitted under this Warrant shall be given in writing and shall be deemed effectively given as hereinafter described (i) if given by personal delivery, then such notice shall be deemed given upon such delivery, (ii) if given by telex or facsimile, then such notice shall be deemed given upon receipt of confirmation of complete transmittal, (iii) if given by mail, then such notice shall be deemed given upon the earlier of (A) receipt of such notice by the recipient or (B) three days after such notice is deposited in first class mail, postage prepaid, and (iv) if given by an internationally recognized overnight air courier, then such notice shall be deemed given one business day after delivery to such carrier. All notices shall be addressed as follows: if to the Warrantholder, at its address as set forth in the Company’s books and records and, if to the Company, at the address as follows, or at such other address as the Warrantholder or the Company may designate by ten days’ advance written notice to the other:

If to the Company:

GeoResources, Inc.

110 Cypress Station Drive

Suite 220

Houston, TX 77090

Fax: 281 ###-###-####

Attention: Frank A. Lodzinski, President

With a copy to:

Jones & Keller, P.C.

1625 Broadway, 16^th Floor

Denver, CO 80202

Fax: 303 ###-###-####

Attention: Reid A. Godbolt, Esq.

Section 14. Registration Rights. The initial Warrantholder is entitled to the benefit of certain registration rights with respect to the shares of Common Stock issuable upon the exercise of this Warrant as provided in the Registration Rights Agreement, and any subsequent Warrantholder may be entitled to such rights.

Section 15. Successors. All the covenants and provisions hereof by or for the benefit of the Warrantholder shall bind and inure to the benefit of its respective successors and assigns hereunder.

Section 16. Governing Law; Consent to Jurisdiction; Waiver of Jury Trial. This Warrant shall be governed by, and construed in accordance with, the internal laws of the State of New York, without reference to the choice of law provisions thereof. The Company and, by accepting this Warrant, the Warrantholder, each irrevocably submits to the exclusive jurisdiction of the courts of the State of New York located in New York County and the United States District Court for the Southern District of New York for the purpose of any suit, action,

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proceeding or judgment relating to or arising out of this Warrant and the transactions contemplated hereby. Service of process in connection with any such suit, action or proceeding may be served on each party hereto anywhere in the world by the same methods as are specified for the giving of notices under this Warrant. The Company and, by accepting this Warrant, the Warrantholder, each irrevocably consents to the jurisdiction of any such court in any such suit, action or proceeding and to the laying of venue in such court. The Company and, by accepting this Warrant, the Warrantholder, each irrevocably waives any objection to the laying of venue of any such suit, action or proceeding brought in such courts and irrevocably waives any claim that any such suit, action or proceeding brought in any such court has been brought in an inconvenient forum. EACH OF THE COMPANY AND, BY ITS ACCEPTANCE HEREOF, THE WARRANTHOLDER HEREBY WAIVES ANY RIGHT TO REQUEST A TRIAL BY JURY IN ANY LITIGATION WITH RESPECT TO THIS WARRANT AND REPRESENTS THAT COUNSEL HAS BEEN CONSULTED SPECIFICALLY AS TO THIS WAIVER.

Section 17. No Rights as Stockholder. Prior to the exercise of this Warrant, the Warrantholder shall not have or exercise any rights as a stockholder of the Company by virtue of its ownership of this Warrant.

Section 18. Amendment; Waiver. This Warrant is one of a series of Warrants of like tenor issued by the Company pursuant to the Purchase Agreement and initially covering an aggregate of 613,336 shares of Common Stock (collectively, the “Company Warrants”). Any term of this Warrant may be amended or waived (including the adjustment provisions included in Section 8 of this Warrant) upon the written consent of the Company and the holders of Company Warrants representing at least 50% of the number of shares of Common Stock then subject to all outstanding Company Warrants (the “Majority Holders”); provided, that (x) any such amendment or waiver must apply to all Company Warrants; and (y) the number of Warrant Shares subject to this Warrant, the Exercise Price and the Expiration Date may not be amended, and the right to exercise this Warrant may not be altered or waived, without the written consent of the Warrantholder.

Section 19. Section Headings. The section headings in this Warrant are for the convenience of the Company and the Warrantholder and in no way alter, modify, amend, limit or restrict the provisions hereof.

[Signature Page Follows]

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IN WITNESS WHEREOF, the Company has caused this Warrant to be duly executed, as of the 9^th day of June, 2008.

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APPENDIX A

GEORESOURCES, INC.

WARRANT EXERCISE FORM

To [Name] :

The undersigned hereby irrevocably elects to exercise the right of purchase represented by the within Warrant (“Warrant”) for, and to purchase thereunder by the payment of the Exercise Price and surrender of this Warrant,              shares of Common Stock (“Warrant Shares”) provided for therein, and requests that certificates for the Warrant Shares be issued as follows:

and, if the number of Warrant Shares shall not be all the Warrant Shares purchasable upon exercise of this Warrant, that a new Warrant for the balance of the Warrant Shares purchasable upon exercise of this Warrant be registered in the name of the undersigned Warrantholder or the undersigned’s Assignee as below indicated and delivered to the address stated below.

Notwithstanding anything to the contrary contained herein, this Exercise Notice shall constitute a representation by the Warrantholder of the Warrant submitting this Exercise Notice that, after giving effect to the exercise provided for in this Exercise Notice, such Warrantholder (together with its affiliates) will not have beneficial ownership (together with the beneficial ownership of such Person’s affiliates) of a number of shares of Common Stock which exceeds 4.99% of the total outstanding shares of Common Stock as determined pursuant to the provisions of Section 3(c) of this Warrant. In determining whether the Warrantholder (together with its affiliates) will not have beneficial ownership (together with the beneficial ownership of the Warrantholder’s affiliates) of a number of shares of Common Stock which exceeds 4.99%, the Company may rely on the above representation and warranty of the Warrantholder.

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Dated:                    ,             

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APPENDIX B

GEORESOURCES, INC.

NET ISSUE ELECTION NOTICE

To: [Name]

Date: [                            ]

The undersigned hereby elects under Section 3(d) of this Warrant to surrender the right to purchase [            ] shares of Common Stock pursuant to this Warrant and hereby requests the issuance of [            ] shares of Common Stock. The certificate(s) for the shares issuable upon such net issue election shall be issued in the name of the undersigned or as otherwise indicated below.

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