WARRANT TO PURCHASE STOCK

Exhibit 4.2

THIS WARRANT AND THE SHARES ISSUABLE HEREUNDER HAVE NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED (THE “ACT”), OR THE SECURITIES LAWS OF ANY STATE AND, EXCEPT AND PURSUANT TO THE PROVISIONS OF ARTICLE 5 BELOW, MAY NOT BE OFFERED, SOLD OR OTHERWISE TRANSFERRED, PLEDGED OR HYPOTHECATED UNLESS AND UNTIL REGISTERED UNDER SAID ACT AND APPLICABLE STATE SECURITIES LAW OR, IN THE OPINION OF LEGAL COUNSEL IN FORM AND SUBSTANCE SATISFACTORY TO THE ISSUER OF THESE SECURITIES, SUCH OFFER, SALE OR TRANSFER, PLEDGE OR HYPOTHECATION IS EXEMPT FROM REGISTRATION.

WARRANT TO PURCHASE STOCK

Company: Exa Corporation, a Delaware corporation

Number of Shares: As set forth below

Class of Stock: Series G Convertible Preferred Stock, $0.001 par value per share

Warrant Price: $0.94, subject to adjustment

Issue Date: January 28, 2011

Expiration Date: January 27, 2021

THIS WARRANT CERTIFIES THAT, for good and valuable consideration, GOLD HILL CAPITAL 2008, L.P. (together with any successor or permitted assignee or transferee of this Warrant or of any shares issued upon exercise hereof, “Holder”) is entitled to purchase up to such number of fully paid and non-assessable shares of the above-stated Class of Stock (the “Class”) of the above-named company (the “Company”) as determined below, at the above-stated Warrant Price per Share, all as set forth above and as adjusted pursuant to Article 2 of this Warrant, subject to the provisions and upon the terms and conditions set forth in this Warrant.

A. Number of Shares. Upon the date of each Growth Capital Advance (as defined in the Loan Agreement) made by Holder (or its affiliate) to the Company under the Loan Agreement, this Warrant automatically shall become exercisable for such number of shares of the Class (cumulatively, the “Shares”) as shall equal (1)(a) 0.1316, multiplied by (b) the amount of such Growth Capital Advance made by Holder (or its affiliate), divided by (2) the Warrant Price in effect on and as of the date of such Growth Capital Advance, as may be adjusted thereafter from time to time in accordance with the provisions of this Warrant.

ARTICLE 1. EXERCISE.

1.1 Method of Exercise. Holder may exercise this Warrant by delivering the original of this Warrant together with a duly executed Notice of Exercise in substantially the form attached as Appendix 1 to the principal office of the Company. Unless Holder is exercising the conversion right set forth in Article 1.2, Holder shall also deliver to the Company a check, wire transfer (to an account designated by the Company), or other form of payment acceptable to the Company for the aggregate Warrant Price for the Shares being purchased.

1.2 Conversion Right. In lieu of exercising this Warrant as specified in Article 1.1, Holder may from time to time convert this Warrant, in whole or in part, into a number of Shares determined by dividing (a) the aggregate fair market value of the Shares or other securities otherwise issuable upon exercise of this Warrant minus the aggregate Warrant Price of such Shares by (b) the fair market value of one Share. The fair market value of the Shares shall be determined pursuant to Article 1.3.

1.3 Fair Market Value. If the Company’s common stock is traded in a public market and the Shares are common stock, the fair market value of a Share shall be the closing price of a share of common stock reported for the business day immediately before Holder delivers this Warrant together with its Notice of Exercise to the Company (or in the instance where the Warrant is exercised immediately prior to the effectiveness of the Company’s initial public offering (“IPO”), the “price to public” per share price specified in the final prospectus relating to such offering). If the Company’s common stock is traded in a public market and the Shares are preferred stock, the fair market value of a Share shall be the closing price of a share of the Company’s common stock reported for the business day immediately before Holder delivers this Warrant together with its Notice of Exercise to the Company (or, in the instance where the Warrant is exercised immediately prior to the effectiveness of the IPO, the initial “price to public” per share price specified in the final prospectus relating to such offering), in both cases, multiplied by the number of shares of the Company’s common stock into which a Share is then convertible. If the Company’s common stock is not traded in a public market, the Board of Directors of the Company shall determine fair market value of a Share in its reasonable good faith judgment.

1.4 Delivery of Certificate and New Warrant. Promptly after Holder exercises or converts this Warrant and, if applicable, the Company receives payment of the aggregate Warrant Price, the Company shall deliver to Holder certificates for the Shares acquired and, if this Warrant has not been fully exercised or converted and has not expired, a new warrant of like tenor representing the Shares not so acquired.

1.5 Replacement of Warrants. On receipt of evidence reasonably satisfactory to the Company of the loss, theft, destruction or mutilation of this Warrant and, in the case of loss, theft or destruction, on delivery of an indemnity agreement reasonably satisfactory in form and amount to the Company or, in the case of mutilation, on surrender and cancellation of this Warrant, the Company shall execute and deliver, in lieu of this Warrant, a new warrant of like tenor.

1.6 Treatment of Warrant Upon Acquisition of Company.

1.6.1 “Acquisition”. For the purpose of this Warrant, “Acquisition” means any sale, assignment, transfer or other disposition of all or substantially all of the assets of the Company, or any reorganization, consolidation, merger, or sale of outstanding equity securities of the Company by the holders thereof, where the holders of the Company’s outstanding voting equity securities as of immediately before such transaction beneficially own less than a majority of the outstanding voting equity securities of the surviving or successor entity as of immediately after such transaction.

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1.6.2 Treatment of Warrant at Acquisition.

A) Holder agrees that, in the event of an Acquisition in which the sole consideration that would be received by received by the Holder in respect of the Shares were it to exercise or convert this Warrant in full prior to the closing thereof is cash and/or Marketable Securities, this Warrant shall terminate on and as of the closing of such Acquisition to the extent not previously exercised. The Company shall provide Holder with written notice of any proposed Acquisition not later than ten (10) days prior to the closing thereof setting forth the material terms and conditions thereof, and shall provide Holder with copies of the draft transaction agreements and other documents in connection therewith and with such other information respecting such proposed Acquisition as may reasonably be requested by Holder.

B) Upon the closing of any Acquisition other than as particularly described in subsection (A) above, the surviving or successor entity shall assume this Warrant and the obligations of the Company hereunder, and this Warrant shall, from and after such closing, be exercisable for the same class, number and kind of securities, cash and other property as would have been paid for or in respect of the Shares issuable (as of immediately prior to such closing) upon exercise in full hereof as if such Shares had been issued and outstanding on and as of such closing, at an aggregate Warrant Price equal to the aggregate Warrant Price in effect as of immediately prior to such closing; provided, that the provisions of Article 3.3 hereof shall terminate as of the closing of the Acquisition.

C) As used in this Article 1.6, “Marketable Securities” means securities meeting all of the following requirements: (i) the issuer thereof is then subject to the reporting requirements of Section 13 or Section 15(d) of the Securities Exchange Act of 1934, as amended (the “Exchange Act”), and is then current in its filing of all required reports and other information under the Act and the Exchange Act; and (ii) the class and series of shares or other security of the issuer that would be received by Holder in connection with the Acquisition were Holder to exercise or convert this Warrant on or prior to the closing thereof is then traded on a national securities exchange or over-the-counter market.

D) In the event of an Acquisition described in subsection (B) above, the Board of Directors of the Company may, in its discretion take any one or more of the following actions as to this Warrant: (i) provide that this Warrant shall be assumed, or an equivalent Warrant shall be substituted, by the acquiring or succeeding corporation (or an affiliate thereof), or (ii) upon ten (10) days prior written notice to the Holder provide that this Warrant will terminate immediately prior to the consummation of the Acquisition unless exercised by the Holder within a specified period following the date of such notice.

ARTICLE 2. ADJUSTMENTS TO THE SHARES.

2.1 Stock Splits, Etc. If the Company subdivides the outstanding shares of the Class by reclassification or otherwise into a greater number of shares, the number of Shares purchasable hereunder shall be proportionately increased and the Warrant Price shall be proportionately decreased. If the outstanding shares of the Class are combined or consolidated, by reclassification or otherwise, into a lesser number of shares, the Warrant Price shall be proportionately increased and the number of Shares shall be proportionately decreased.

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2.2 Reclassification, Exchange, Combinations or Substitution. Upon any reclassification, exchange, substitution, or similar event affecting the outstanding shares of the Class, Holder shall be entitled to receive, upon exercise or conversion of this Warrant, the number and kind of securities and property that Holder would have received for the Shares if this Warrant had been exercised immediately before such reclassification, exchange, substitution, or similar event. Such an event shall include, without limitation, any automatic conversion of the outstanding or issuable securities of the Company of the same class or series as the Shares to common stock pursuant to the terms of the Company’s Certificate of Incorporation. The Company or its successor shall promptly issue to Holder a certificate pursuant to Article 2.6 hereof setting forth the number, class and series or other designation of such new securities or other property issuable upon exercise or conversion of this Warrant as a result of such reclassification, exchange, substitution or other event. The provisions of this Article 2.2 shall similarly apply to successive reclassifications, exchanges, substitutions, or other events.

2.3 Adjustments for Diluting Issuances. The number of shares of common stock issuable upon conversion of the Shares shall be subject to adjustment from time to time in the manner set forth in the Company’s Certificate of Incorporation as if the Shares were issued and outstanding on and as of the date of any such required adjustment. The provisions set forth for the Class in the Company’s Certificate of Incorporation relating to the above in effect as of the Issue Date may not be amended, modified or waived, without the prior written consent of Holder unless such amendment, modification or waiver affects the rights associated with the Shares in the same manner as such amendment, modification or waiver affects the rights associated with all other shares of the Class.

2.4 No Impairment. The Company shall not, by amendment of its Certificate of Incorporation or through a reorganization, transfer of assets, consolidation, merger, dissolution, issue, or sale of securities or any other voluntary action, avoid or seek to avoid the observance or performance of any of the terms to be observed or performed under this Warrant by the Company, but shall at all times in good faith assist in carrying out of all the provisions of this Article 2 and in taking all such action as may reasonably be necessary or appropriate to protect Holder’s rights under this Article against impairment.

2.5 Fractional Shares. No fractional Shares shall be issuable upon exercise or conversion of the Warrant and the number of Shares to be issued shall be rounded down to the nearest whole Share. If a fractional share interest arises upon any exercise or conversion of the Warrant, the Company shall eliminate such fractional share interest by paying Holder the amount computed by multiplying the fractional interest by the fair market value of a full Share.

2.6 Certificate as to Adjustments. Upon each adjustment of the Warrant Price, Class and/or number of Shares, the Company shall promptly notify Holder in writing, and, at the Company’s expense, promptly compute such adjustment, and furnish Holder with a certificate of its Chief Financial Officer setting forth such adjustment and the facts upon which such adjustment is based. The Company shall, upon written request (but not more than once in any calendar quarter), furnish Holder a certificate setting forth the Warrant Price, Class and number of Shares in effect upon the date thereof and the series of adjustments leading to such Warrant Price, Class and number of Shares.

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2.7 Pay to Play Adjustments. Notwithstanding the definition of Class herein, if Pay to Play Provisions are at any time during the term of this Warrant and prior to any exercise hereof applied to the outstanding shares of the Class, then from and after such application and prior to such exercise, “Class,” for purposes of the Shares issuable upon exercise of the unexercised portion hereof, shall mean that class and series of the Company’s securities that a holder of outstanding shares of the Class as of immediately prior to such application would have received or retained had such holder participated in the manner necessary to receive or retain the class and series of the Company’s securities having the relative rights, powers, privileges and preferences more favorable to the holder. As used herein, “Pay to Play Provisions” means provisions set forth in the Company’s Certificate of Incorporation or elsewhere that require holders of the outstanding shares of the Class to participate in a subsequent round of equity financing of the Company or lose all or a portion of the benefit of anti-dilution protection or any other right, power, privilege or preference applicable to such shares or have such shares automatically convert to common stock or another class or series of Company capital stock.

ARTICLE 3. REPRESENTATIONS AND COVENANTS OF THE COMPANY.

3.1 Representations, Warranties and Agreements. The Company represents and warrants to, and agrees with, the Holder as follows:

(a) The Company shall at all times during the term of this Warrant keep reserved out of its authorized and unissued capital stock a sufficient number of shares of the Class (and, if the Class is a series of convertible preferred stock, a sufficient number of shares of common stock) to permit exercise in full of this Warrant and, if applicable, conversion of the Shares issuable and issued upon any exercise hereof. All Shares which may be issued upon the exercise or conversion of this Warrant shall, upon issuance, be duly authorized, validly issued, fully paid and non-assessable, and free of any liens and encumbrances except for restrictions on transfer provided for herein or under applicable federal and state securities laws.

(b) The Company’s capitalization table attached hereto as Schedule 1 is true and complete as of the Issue Date.

3.2 Notice of Certain Events. If the Company proposes at any time (a) to declare any dividend or distribution upon the outstanding shares of the Class, whether in cash, property, stock, or other securities and whether or not a regular cash dividend; (b) to offer for subscription or sale pro rata to the holders of the outstanding shares of the Class any additional shares of any class or series of the Company’s stock (other than pursuant to contractual pre-emptive rights); (c) to effect any reclassification, reorganization or recapitalization of the shares of the Class; (d) to effect an Acquisition or to liquidate, dissolve or wind up; or (e) offer holders of registration rights the opportunity to participate in an underwritten public offering of the Company’s securities for cash, then, in connection with each such event, the Company shall give Holder: (1) at least 10 days prior written notice of the date on which a record will be taken for such dividend, distribution, or subscription rights (and specifying the date on which the holders

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of shares of the Class will be entitled thereto) or for determining rights to vote, if any, in respect of the matters referred to in (c) and (d) above; (2) in the case of the matters referred to in (c) and (d) above at least 10 days prior written notice of the date when the same is expected to take place (and specifying the expected date on which the holders of shares of the Class will be entitled to exchange their shares for the securities or other property deliverable upon the occurrence of such event); and (3) in the case of the matter referred to in (e) above, the same notice as is given to the holders of such registration rights.

3.3 Registration Rights. The Company agrees that the Shares, after conversion thereof into common stock of the Company, shall have “Piggyback” and S-3 registration rights substantially similar to such rights in the registration rights sections of that certain Purchase Agreement dated as of April 30, 2008 by and among the Company and the Investors named therein (as amended and in effect from time to time, the “Rights Agreement”). The provisions set forth in the Rights Agreement relating to the foregoing registration rights in effect as of the Issue Date may not be amended, modified or waived without the prior written consent of Holder unless such amendment, modification or waiver affects the rights associated with the Shares in the same manner as such amendment, modification, or waiver affects the rights associated with all other shares of the Class whose holders are parties thereto. Upon the Company’s request, Holder shall become a party to the applicable registration rights sections of the Rights Agreement, by execution and delivery between the parties of a joinder agreement, counterpart signature page or the like, for purposes of further implementing the registration rights granted to Holder in this Article 3.3.

3.4 No Shareholder Rights. Except as provided in this Warrant, Holder will not have any rights as a shareholder of the Company until the exercise of this Warrant.

3.5 Certain Information. At all times prior to the IPO, the Company agrees to provide Holder at any time and from time to time with such information as Holder may reasonably request for purposes of Holder’s compliance with regulatory, accounting and reporting requirements applicable to Holder. Holder agrees to treat and hold all such information in confidence in accordance with the provisions of Section 12.9 of the Loan Agreement.

ARTICLE 4. REPRESENTATIONS, WARRANTIES OF THE HOLDER. The Holder represents and warrants to the Company as follows:

4.1 Purchase for Own Account. This Warrant and the securities to be acquired upon exercise of this Warrant by Holder will be acquired for investment for Holder’s account, not as a nominee or agent, and not with a view to the public resale or distribution within the meaning of the Act. Holder also represents that it has not been formed for the specific purpose of acquiring this Warrant or the Shares.

4.2 Disclosure of Information. Holder has received or has had full access to all the information it considers necessary or appropriate to make an informed investment decision with respect to the acquisition of this Warrant and its underlying securities. Holder further has had an opportunity to ask questions and receive answers from the Company regarding the terms and conditions of the offering of this Warrant and its underlying securities and to obtain additional information (to the extent the Company possessed such information or could acquire it without unreasonable effort or expense) necessary to verify any information furnished to Holder or to which Holder has access.

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4.3 Investment Experience. Holder understands that the purchase of this Warrant and its underlying securities involves substantial risk. Holder has experience as an investor in securities of companies in the development stage and acknowledges that Holder can bear the economic risk of such Holder’s investment in this Warrant and its underlying securities and has such knowledge and experience in financial or business matters that Holder is capable of evaluating the merits and risks of its investment in this Warrant and its underlying securities and/or has a preexisting personal or business relationship with the Company and certain of its officers, directors or controlling persons of a nature and duration that enables Holder to be aware of the character, business acumen and financial circumstances of such persons.

4.4 Accredited Investor Status. Holder is an “accredited investor” within the meaning of Regulation D promulgated under the Act.

4.5 The Act. Holder understands that this Warrant and its underlying securities have not been registered under the Act in reliance upon a specific exemption therefrom, which exemption depends upon, among other things, the bona fide nature of the Holder’s investment intent as expressed herein. Holder understands that this Warrant and the Shares issued upon any exercise or conversion hereof must be held indefinitely unless subsequently registered under the Act and qualified under applicable state securities laws, or unless exemption from such registration and qualification are otherwise available.

ARTICLE 5. MISCELLANEOUS.

5.1 Term: This Warrant is exercisable in whole or in part at any time and from time to time on or before the Expiration Date.

5.2 Legend. Each certificate representing Shares issued upon any exercise or conversion hereof (and the certificates representing the securities issued upon conversion of such Shares, if any) shall be imprinted with a legend in substantially the following form:

THE SECURITIES REPRESENTED BY THIS CERTIFICATE HAVE NOT BEEN REGISTERED UNDER THE SECURITES ACT OF 1933, AS AMENDED (THE “ACT”), OR THE SECURITIES LAWS OF ANY STATE AND, EXCEPT AND PURSUANT TO THE PROVISIONS OF ARTICLE 5 OF THAT CERTAIN WARRANT TO PURCHASE STOCK ISSUED BY THE COMPANY TO GOLD HILL CAPITAL 2008, L.P. DATED AS OF JANUARY __, 2011, MAY NOT BE OFFERED, SOLD OR OTHERWISE TRANSFERRED, PLEDGED OR HYPOTHECATED UNLESS AND UNTIL REGISTERED UNDER SAID ACT AND APPLICABLE STATE SECURITIES LAW OR, IN THE OPINION OF LEGAL COUNSEL IN FORM AND SUBSTANCE SATISFACTORY TO THE ISSUER OF THESE SECURITIES, SUCH OFFER, SALE OR TRANSFER, PLEDGE OR HYPOTHECATION IS EXEMPT FROM REGISTRATION.

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5.3 Compliance with Securities Laws on Transfer. This Warrant and the Shares issuable upon exercise of this Warrant (and the securities issuable, directly or indirectly, upon conversion of the Shares, if any) may not be transferred or assigned in whole or in part without compliance with applicable federal and state securities laws by the transferor and the transferee (including, without limitation, the delivery of investment representation letters and legal opinions reasonably satisfactory to the Company, as reasonably requested by the Company). The Company shall not require Holder to provide an opinion of counsel if the transfer is to an affiliate of Holder, provided that such affiliate transferee is an “accredited investor” as defined in Regulation D promulgated under the Act. Any such affiliate transferee shall, upon its receipt of this Warrant and/or any Shares (or any securities issued upon conversion of such Shares), be deemed to have made each of the representations and warranties to the Company set forth in Article 4 above.

5.4 Transfer Procedure. Subject to the provisions of Article 5.3 and upon providing the Company with written notice, Holder may transfer all or part of this Warrant or the Shares issuable upon exercise of this Warrant (or the securities issuable directly or indirectly, upon conversion of the Shares, if any) to any transferee, provided, however, in connection with any such transfer, Holder will give the Company notice of the portion of the Warrant being transferred with the name, address and taxpayer identification number of the transferee and Holder will surrender this Warrant to the Company for reissuance to the transferee(s) (and Holder if applicable). At all times prior to the IPO or in connection with an Acquisition, the Company may refuse to transfer this Warrant or the Shares to any person or entity who directly competes with the Company.

5.5 Notices. All notices and other communications from the Company to the Holder, or vice versa, shall be deemed delivered and effective when given personally or mailed by first-class registered or certified mail, postage prepaid (or on the first business day after transmission by facsimile), at such address as may have been furnished to the Company or Holder, as the case may be, in writing by the Company or such holder from time to time. All notices to Holder shall be addressed as follows until the Company receives notice of a change of address in connection with a transfer or otherwise:

Gold Hill Capital 2008, L.P.

Attn: Mr. David Fischer

Two Newton Executive Park

Suite 203

2227 Washington Street

Newton, Massachusetts 02462

Telephone: 617 ###-###-####

Facsimile: 617 ###-###-####

Notice to the Company shall be addressed as follows until Holder receives notice of a change in address:

Exa Corporation

Attn: Chief Financial Officer

55 Network Drive

Burlington, MA 01803

Telephone: 781 ###-###-####

Facsimile: 781 ###-###-####

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5.6 Waiver. This Warrant and any term hereof may be changed, waived, discharged or terminated only by an instrument in writing signed by the party against which enforcement of such change, waiver, discharge or termination is sought.

5.7 Attorney’s Fees. In the event of any dispute between the parties concerning the terms and provisions of this Warrant, the party prevailing in such dispute shall be entitled to collect from the other party all costs incurred in such dispute, including reasonable attorneys’ fees.

5.8 Counterparts. This Warrant may be executed in counterparts, all of which together shall constitute one and the same agreement.

5.9 Governing Law. This Warrant shall be governed by and construed in accordance with the Delaware General Corporation Law, and the laws of the Commonwealth of Massachusetts without giving effect to its principles regarding conflicts of law.

[Remainder of page left blank intentionally; signature page follows]

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IN WITNESS WHEREOF, the parties have caused this Warrant to Purchase Stock to be executed by their duly authorized representatives as of the date first above written.

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APPENDIX 1

NOTICE OF EXERCISE

1. Holder elects to purchase ___________ shares of the Common/Series ______ Preferred [strike one] Stock of __________________ pursuant to the terms of the attached Warrant, and tenders payment of the purchase price of the shares in full.

[or]

1. Holder elects to convert the attached Warrant into Shares/cash [strike one] in the manner specified in the Warrant. This conversion is exercised for _____________________ of the Shares covered by the Warrant.

[Strike paragraph that does not apply.]

2. Please issue a certificate or certificates representing the Shares in the name specified below:

3. By its execution below and for the benefit of the Company, Holder hereby makes each of the representations and warranties in Article 4 of the Warrant as of the date hereof.

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