CERTIFICATE OF DESIGNATIONS of SERIES A JUNIOR PARTICIPATING PREFERRED STOCK of HERCULES OFFSHORE, INC. Pursuant to Section 151 of the General Corporation Law of the State of Delaware

Exhibit 4.2

CERTIFICATE OF DESIGNATIONS

of

SERIES A JUNIOR PARTICIPATING PREFERRED STOCK

of

HERCULES OFFSHORE, INC.

Pursuant to Section 151 of the General Corporation Law

of the State of Delaware

HERCULES OFFSHORE, INC., a corporation organized and existing under the General Corporation Law of the State of Delaware, in accordance with the provisions of Section 103 thereof, DOES HEREBY CERTIFY:

That pursuant to the authority vested in the Board of Directors in accordance with the provisions of the Certificate of Incorporation of the said Corporation, the said Board of Directors has adopted the following resolution creating a series of 2,000,000 shares of Preferred Stock designated as “Series A Junior Participating Preferred Stock”:

RESOLVED, that pursuant to the authority vested in the Board of Directors of this Corporation in accordance with the provisions of the Certificate of Incorporation, a series of Preferred Stock, par value $0.01 per share, of the Corporation be and hereby is created, and that the designation and number of shares thereof and the voting and other powers, preferences and relative, participating, optional or other rights of the shares of such series and the qualifications, limitations and restrictions thereof are as follows:

Series A Junior Participating Preferred Stock

1. Designation and Amount. There shall be a series of Preferred Stock that shall be designated as “Series A Junior Participating Preferred Stock,” and the number of shares constituting such series shall be 2,000,000. Such number of shares may be increased or decreased by resolution of the Board of Directors; provided, however, that no decrease shall reduce the number of shares of Series A Junior Participating Preferred Stock to less than the number of shares then issued and outstanding plus the number of shares issuable upon exercise of outstanding rights, options or warrants or upon conversion of outstanding securities issued by the Corporation.

2. Dividends and Distributions.

(A) Subject to the prior and superior rights of the holders of any shares of any series of Preferred Stock ranking prior and superior to the shares of Series A Junior Participating Preferred Stock with respect to dividends, the holders of shares of Series A Junior Participating Preferred Stock, in preference to the holders of shares of any class or series of stock of the Corporation ranking junior to the Series A Junior Participating Preferred Stock, shall be entitled to receive, when, as and if declared by the Board of Directors out of funds legally available for

1

the purpose, quarterly dividends payable in cash on March 31, June 30, September 30 and December 31 in each year (each such date being referred to herein as a “Quarterly Dividend Payment Date”), commencing on the first Quarterly Dividend Payment Date after the first issuance of a share or fraction of a share of Series A Junior Participating Preferred Stock, in an amount per share (rounded to the nearest cent) equal to the greater of (a) $1.00 or (b) the Adjustment Number (as defined below) times the aggregate per share amount of all cash dividends, and the Adjustment Number times the aggregate per share amount (payable in kind) of all non-cash dividends or other distributions other than a dividend payable in shares of Common Stock or a subdivision of the outstanding shares of Common Stock (by reclassification or otherwise), declared on the Common Stock, par value $0.01 per share, of the Corporation (the “Common Stock”) since the immediately preceding Quarterly Dividend Payment Date, or, with respect to the first Quarterly Dividend Payment Date, since the first issuance of any share or fraction of a share of Series A Junior Participating Preferred Stock. The “Adjustment Number” shall initially be 100. In the event the Corporation shall at any time after November 1, 2005 (i) declare any dividend on Common Stock payable in shares of Common Stock, (ii) subdivide the outstanding Common Stock or (iii) combine the outstanding Common Stock into a smaller number of shares, then in each such case the Adjustment Number in effect immediately prior to such event shall be adjusted by multiplying such Adjustment Number by a fraction the numerator of which is the number of shares of Common Stock outstanding immediately after such event and the denominator of which is the number of shares of Common Stock that were outstanding immediately prior to such event.

(B) The Corporation shall declare a dividend or distribution on the Series A Junior Participating Preferred Stock as provided in paragraph (A) above immediately after it declares a dividend or distribution on the Common Stock (other than a dividend payable in shares of Common Stock); provided that, in the event no dividend or distribution shall have been declared on the Common Stock during the period between any Quarterly Dividend Payment Date and the next subsequent Quarterly Dividend Payment Date, a dividend of $1.00 per share on the Series A Junior Participating Preferred Stock shall nevertheless be payable on such subsequent Quarterly Dividend Payment Date.

(C) Dividends shall begin to accrue and be cumulative on outstanding shares of Series A Junior Participating Preferred Stock from the Quarterly Dividend Payment Date next preceding the date of issue of such shares of Series A Junior Participating Preferred Stock, unless the date of issue of such shares is prior to the record date for the first Quarterly Dividend Payment Date, in which case dividends on such shares shall begin to accrue from the date of issue of such shares, or unless the date of issue is a Quarterly Dividend Payment Date or is a date after the record date for the determination of holders of shares of Series A Junior Participating Preferred Stock entitled to receive a quarterly dividend and before such Quarterly Dividend Payment Date, in either of which events such dividends shall begin to accrue and be cumulative from such Quarterly Dividend Payment Date. Accrued but unpaid dividends shall not bear interest. Dividends paid on the shares of Series A Junior Participating Preferred Stock in an amount less than the total amount of such dividends at the time accrued and payable on such shares shall be allocated pro rata on a share-by-share basis among all such shares at the time outstanding. The Board of Directors may fix a record date for the determination of holders of shares of Series A Junior Participating Preferred Stock entitled to receive payment of a dividend

2

or distribution declared thereon, which record date shall be no more than 30 days prior to the date fixed for the payment thereof.

3. Voting Rights. The holders of shares of Series A Junior Participating Preferred Stock shall have the following voting rights:

(A) Each share of Series A Junior Participating Preferred Stock shall entitle the holder thereof to a number of votes equal to the Adjustment Number on all matters submitted to a vote of the stockholders of the Corporation.

(B) Except as otherwise provided herein, in the Certificate of Incorporation or by law, the holders of shares of Series A Junior Participating Preferred Stock, the holders of shares of any other class or series entitled to vote with the Common Stock and the holders of shares of Common Stock shall vote together as one class on all matters submitted to a vote of stockholders of the Corporation.

(C) (i) If at any time dividends on any Series A Junior Participating Preferred Stock shall be in arrears in an amount equal to six quarterly dividends thereon, the occurrence of such contingency shall mark the beginning of a period (herein called a “default period”) that shall extend until such time when all accrued and unpaid dividends for all previous quarterly dividend periods and for the current quarterly dividend period on all shares of Series A Junior Participating Preferred Stock then outstanding shall have been declared and paid or set apart for payment. During each default period, (1) the number of Directors shall be increased by two, effective as of the time of election of such Directors as herein provided, and (2) the holders of Preferred Stock (including holders of the Series A Junior Participating Preferred Stock) upon which these or like voting rights have been conferred and are exercisable (the “Voting Preferred Stock”) with dividends in arrears in an amount equal to six quarterly dividends thereon, voting as a class, irrespective of series, shall have the right to elect such two Directors.

(ii) During any default period, such voting right of the holders of Series A Junior Participating Preferred Stock may be exercised initially at a special meeting called pursuant to subparagraph (iii) of this Section 3(C) or at any annual meeting of stockholders, and thereafter at annual meetings of stockholders, provided that such voting right shall not be exercised unless the holders of at least one-third in number of the shares of Voting Preferred Stock outstanding shall be present in person or by proxy. The absence of a quorum of the holders of Common Stock shall not affect the exercise by the holders of Voting Preferred Stock of such voting right.

(iii) Unless the holders of Voting Preferred Stock shall, during an existing default period, have previously exercised their right to elect Directors, the Board of Directors may order, or any stockholder or stockholders owning in the aggregate not less than ten percent of the total number of shares of Voting Preferred Stock outstanding, irrespective of series, may request, the calling of a special meeting of the holders of Voting Preferred Stock, which meeting shall thereupon be called by the Chairman of the Board, the President, a Vice President or the Secretary of the Corporation. Notice of such meeting and of any annual meeting at which holders of Voting Preferred Stock are entitled to vote pursuant to this paragraph (C)(iii) shall be given to each holder of record of Voting Preferred Stock by mailing a copy of such notice to him

3

at his last address as the same appears on the books of the Corporation. Such meeting shall be called for a time not earlier than 20 days and not later than 60 days after such order or request or, in default of the calling of such meeting within 60 days after such order or request, such meeting may be called on similar notice by any stockholder or stockholders owning in the aggregate not less than ten percent of the total number of shares of Voting Preferred Stock outstanding. Notwithstanding the provisions of this paragraph (C)(iii), no such special meeting shall be called during the period within 60 days immediately preceding the date fixed for the next annual meeting of the stockholders.

(iv) In any default period, after the holders of Voting Preferred Stock shall have exercised their right to elect Directors voting as a class, (x) the Directors so elected by the holders of Voting Preferred Stock shall continue in office until their successors shall have been elected by such holders or until the expiration of the default period, and (y) any vacancy in the Board of Directors may be filled by vote of a majority of the remaining Directors theretofore elected by the holders of the class or classes of stock which elected the Director whose office shall have become vacant. References in this paragraph (C) to Directors elected by the holders of a particular class or classes of stock shall include Directors elected by such Directors to fill vacancies as provided in clause (y) of the foregoing sentence.

(v) Immediately upon the expiration of a default period, (x) the right of the holders of Voting Preferred Stock as a class to elect Directors shall cease, (y) the term of any Directors elected by the holders of Voting Preferred Stock as a class shall terminate and (z) the number of Directors shall be such number as may be provided for in the Certificate of Incorporation or By-Laws irrespective of any increase made pursuant to the provisions of paragraph (C) of this Section 3 (such number being subject, however, to change thereafter in any manner provided by law or in the Certificate of Incorporation or By-Laws). Any vacancies in the Board of Directors effected by the provisions of clauses (y) and (z) in the preceding sentence may be filled by a majority of the remaining Directors.

(D) Except as set forth herein, holders of Series A Junior Participating Preferred Stock shall have no special voting rights and their consent shall not be required (except to the extent they are entitled to vote with holders of Common Stock as set forth herein) for taking any corporate action.

4. Certain Restrictions.

(A) Whenever quarterly dividends or other dividends or distributions payable on the Series A Junior Participating Preferred Stock as provided in Section 2 are in arrears, thereafter and until all accrued and unpaid dividends and distributions, whether or not declared, on shares of Series A Junior Participating Preferred Stock outstanding shall have been paid in full, the Corporation shall not

(i) declare or pay dividends on, make any other distributions on, or redeem or purchase or otherwise acquire for consideration any shares of stock ranking junior (either as to dividends or upon liquidation, dissolution or winding up) to the Series A Junior Participating Preferred Stock;

4

(ii) declare or pay dividends on or make any other distributions on any shares of stock ranking on a parity (either as to dividends or upon liquidation, dissolution or winding up) with the Series A Junior Participating Preferred Stock, except dividends paid ratably on the Series A Junior Participating Preferred Stock and all such parity stock on which dividends are payable or in arrears in proportion to the total amounts to which the holders of all such shares are then entitled; or

(iii) redeem or purchase or otherwise acquire for consideration any shares of Series A Junior Participating Preferred Stock, or any shares of stock ranking on a parity with the Series A Junior Participating Preferred Stock, except in accordance with a purchase offer made in writing or by publication (as determined by the Board of Directors) to all holders of Series A Junior Participating Preferred Stock, or to all such holders and the holders of any such shares ranking on a parity therewith, upon such terms as the Board of Directors, after consideration of the respective annual dividend rates and other relative rights and preferences of the respective series and classes, shall determine in good faith will result in fair and equitable treatment among the respective series or classes.

(B) The Corporation shall not permit any subsidiary of the Corporation to purchase or otherwise acquire for consideration any shares of stock of the Corporation unless the Corporation could, under paragraph (A) of this Section 4, purchase or otherwise acquire such shares at such time and in such manner.

5. Reacquired Shares. Any shares of Series A Junior Participating Preferred Stock purchased or otherwise acquired by the Corporation in any manner whatsoever shall be retired and canceled promptly after the acquisition thereof. All such shares shall upon their cancellation become authorized but unissued shares of Preferred Stock and may be reissued as part of a new series of Preferred Stock to be created by resolution or resolutions of the Board of Directors, subject to any conditions and restrictions on issuance set forth herein.

6. Liquidation, Dissolution or Winding Up. (A) Upon any liquidation (voluntary or otherwise), dissolution or winding up of the Corporation, no distribution shall be made to the holders of shares of stock ranking junior (either as to dividends or upon liquidation, dissolution or winding up) to the Series A Junior Participating Preferred Stock unless, prior thereto, the holders of shares of Series A Junior Participating Preferred Stock shall have received $100 per share, plus an amount equal to accrued and unpaid dividends and distributions thereon, whether or not declared, to the date of such payment (the “Series A Junior Participating Preferred Stock Liquidation Preference”). Following the payment of the full amount of the Series A Junior Participating Preferred Stock Liquidation Preference, no additional distributions shall be made to the holders of shares of Series A Junior Participating Preferred Stock unless, prior thereto, the holders of shares of Common Stock shall have received an amount per share (the “Common Adjustment”) equal to the quotient obtained by dividing (i) the Series A Junior Participating Preferred Stock Liquidation Preference by (ii) the Adjustment Number. Following the payment of the full amount of the Series A Junior Participating Preferred Stock Liquidation Preference and the Common Adjustment in respect of all outstanding shares of Series A Junior Participating Preferred Stock and Common Stock, respectively, holders of Series A Junior Participating Preferred Stock and holders of shares of Common Stock shall, subject to the prior rights of all

5

other series of Preferred Stock, if any, ranking prior thereto, receive their ratable and proportionate share of the remaining assets to be distributed in the ratio of the Adjustment Number to 1 with respect to such Series A Junior Participating Preferred Stock and Common Stock, on a per share basis, respectively.

(B) In the event, however, that there are not sufficient assets available to permit payment in full of the Series A Junior Participating Preferred Stock Liquidation Preference and the liquidation preferences of all other series of Preferred Stock, if any, that rank on a parity with the Series A Junior Participating Preferred Stock, then such remaining assets shall be distributed ratably to the holders of such parity shares in proportion to their respective liquidation preferences. In the event, however, that there are not sufficient assets available to permit payment in full of the Common Adjustment, then such remaining assets shall be distributed ratably to the holders of Common Stock.

(C) Neither the merger or consolidation of the Corporation into or with another corporation nor the merger or consolidation of any other corporation into or with the Corporation shall be deemed to be a liquidation, dissolution or winding up of the Corporation within the meaning of this Section 6, but the sale, lease or conveyance of all or substantially all the Corporation’s assets shall be deemed to be a liquidation, dissolution or winding up of the Corporation within the meaning of this Section 6.

7. Consolidation, Merger, etc. In case the Corporation shall enter into any consolidation, merger, combination or other transaction in which the shares of Common Stock are exchanged for or changed into other stock or securities, cash and/or any other property, then in any such case each share of Series A Junior Participating Preferred Stock shall at the same time be similarly exchanged or changed in an amount per share equal to the Adjustment Number times the aggregate amount of stock, securities, cash and/or any other property (payable in kind), as the case may be, into which or for which each share of Common Stock is changed or exchanged.

8. Redemption. (A) The Corporation, at its option, may redeem shares of the Series A Junior Participating Preferred Stock in whole at any time and in part from time to time, at a redemption price equal to the Adjustment Number times the current per share market price (as such term is hereinafter defined) of the Common Stock on the date of the mailing of the notice of redemption, together with unpaid accumulated dividends to the date of such redemption. The “current per share market price” on any date shall be deemed to be the average of the closing price per share of such Common Stock for the ten consecutive Trading Days (as such term is hereinafter defined) immediately prior to such date; provided, however, that in the event that the current per share market price of the Common Stock is determined during a period following the announcement of (A) a dividend or distribution on the Common Stock other than a regular quarterly cash dividend or (B) any subdivision, combination or reclassification of such Common Stock and the ex-dividend date for such dividend or distribution, or the record date for such subdivision, combination or reclassification, shall not have occurred prior to the commencement of such ten Trading Day period, then, and in each such case, the current per share market price shall be properly adjusted to take into account ex-dividend trading. The closing price for each day shall be the last sales price, regular way, or, in case no such sale takes place on such day, the average of the closing bid and asked prices, regular way, in either case as

6

reported in the principal transaction reporting system with respect to securities listed or admitted to trading on the New York Stock Exchange, or, if the Common Stock is not listed or admitted to trading on the New York Stock Exchange, on the principal national securities exchange on which the Common Stock is listed or admitted to trading, or, if the Common Stock is not listed or admitted to trading on any national securities exchange but sales price information is reported for such security, as reported by the National Association of Securities Dealers, Inc. Automated Quotations System (“NASDAQ”) or such other self-regulatory organization or registered securities information processor (as such terms are used under the Securities Exchange Act of 1934, as amended) that then reports information concerning the Common Stock, or, if sales price information is not so reported, the average of the high bid and low asked prices in the over-the-counter market on such day, as reported by NASDAQ or such other entity, or, if on any such date the Common Stock is not quoted by any such entity, the average of the closing bid and asked prices as furnished by a professional market maker making a market in the Common Stock selected by the Board of Directors of the Corporation. If on any such date no such market maker is making a market in the Common Stock, the fair value of the Common Stock on such date as determined in good faith by the Board of Directors of the Corporation shall be used. The term “Trading Day” shall mean a day on which the principal national securities exchange on which the Common Stock is listed or admitted to trading is open for the transaction of business, or, if the Common Stock is not listed or admitted to trading on any national securities exchange but is quoted by NASDAQ, a day on which NASDAQ reports trades, or, if the Common Stock is not so quoted, a Monday, Tuesday, Wednesday, Thursday or Friday on which banking institutions in the State of New York are not authorized or obligated by law or executive order to close.

(B) In the event that fewer than all the outstanding shares of the Series A Junior Participating Preferred Stock are to be redeemed, the number of shares to be redeemed shall be determined by the Board of Directors and the shares to be redeemed shall be determined by lot or pro rata as may be determined by the Board of Directors or by any other method that may be determined by the Board of Directors in its sole discretion to be equitable.

(C) Notice of any such redemption shall be given by mailing to the holders of the shares of Series A Junior Participating Preferred Stock to be redeemed a notice of such redemption, first class postage prepaid, not later than the fifteenth day and not earlier than the sixtieth day before the date fixed for redemption, at their last address as the same shall appear upon the books of the Corporation. Each such notice shall state: (i) the redemption date; (ii) the number of shares to be redeemed and, if fewer than all the shares held by such holder are to be redeemed, the number of such shares to be redeemed from such holder; (iii) the redemption price; (iv) the place or places where certificates for such shares are to be surrendered for payment of the redemption price; and (v) that dividends on the shares to be redeemed will cease to accrue on the close of business on such redemption date. Any notice that is mailed in the manner herein provided shall be conclusively presumed to have been duly given, whether or not the stockholder received such notice, and failure duly to give such notice by mail, or any defect in such notice, to any holder of Series A Junior Participating Preferred Stock shall not affect the validity of the proceedings for the redemption of any other shares of Series A Junior Participating Preferred Stock that are to be redeemed. On or after the date fixed for redemption as stated in such notice, each holder of the shares called for redemption shall surrender the certificate evidencing such shares to the Corporation at the place designated in such notice and shall thereupon be entitled to receive payment of the redemption price. If fewer than all the shares represented by any such

7

surrendered certificate are redeemed, a new certificate shall be issued representing the unredeemed shares.

The shares of Series A Junior Participating Preferred Stock shall not be subject to the operation of any purchase, retirement or sinking fund.

9. Ranking. The Series A Junior Participating Preferred Stock shall rank junior to all other series of the Corporation’s Preferred Stock as to the payment of dividends and the distribution of assets, unless the terms of any such series shall provide otherwise, and shall rank senior to the Common Stock as to such matters.

10. Amendment. At any time that any shares of Series A Junior Participating Preferred Stock are outstanding, the Certificate of Incorporation of the Corporation shall not be amended in any manner which would materially alter or change the powers, preferences or special rights of the Series A Junior Participating Preferred Stock so as to affect them adversely without the affirmative vote of the holders of two-thirds or more of the outstanding shares of Series A Junior Participating Preferred Stock, voting separately as a class.

11. Fractional Shares. Series A Junior Participating Preferred Stock may be issued in fractions of a share that shall entitle the holder, in proportion to such holder’s fractional shares, to exercise voting rights, receive dividends, participate in distributions and to have the benefit of all other rights of holders of Series A Junior Participating Preferred Stock.

8

IN WITNESS WHEREOF, the undersigned has executed this Certificate and does affirm the foregoing as true this 1st day of November, 2005.

9