AMENDMENT AND WAIVER

Exhibit 4.12

AMENDMENT AND WAIVER

THIS AMENDMENT AND WAIVER (this “Amendment and Waiver”) is entered into as of February 15, 2008 by and among Exa Corporation, Delaware corporation (the “Company”), and the undersigned stockholders of the Company (the “Requisite Shareholders”).

WHEREAS, pursuant to the terms of the Purchase Agreements (as defined in Section 6) (i) certain stockholders of the Company have registration rights with respect to certain shares of the Company’s capital stock (“Registration Rights”), and (ii) the Company is required, prior to the issuance by the Company of any of its securities (other than debt securities with no equity feature), to offer to certain stockholders of the Company the right to purchase their Proportionate Percentage (as defined below) of such securities (the “Participation Rights”);

WHEREAS, the Company proposes to enter into a certain Stock Purchase Agreement (the “Series I SPA”; capitalized terms used but not defined herein shall have the meanings ascribed to such terms in the Series I SPA) dated as of the date hereof by and among (i) the Company, (ii) Boston Capital Ventures III, Limited Partnership (“BCV III”) and Boston Capital Ventures IV, Limited Partnership (“BCV IV” and, together with BCV III, “BCV”), and (iii) FMR Corporation (“FMR”) and Fidelity Ventures Ltd. (“Fidelity Ventures” and, together with FMR, “Fidelity”) (collectively, the “Investors”);

WHEREAS, pursuant to the Series I SPA, the Company proposes to (i) issue and sell to the Investors up to an aggregate of 3,378,381 shares of the Company’s Series I Convertible Preferred Stock, $0.001 par value per share (the “Series I Preferred Stock”) at a purchase price of $1.48 per share (the “Cash Financing”), (ii) issue and sell to BCV up to an aggregate of (a) 677,043 shares of the Company’s Series I Preferred Stock and (b) 1,002,024 shares of the Company’s Common Stock, $0.001 par value per share (“Common Stock”), in exchange for the cancellation of indebtedness represented by the Company’s non-convertible promissory notes (the “Non-Convertible Notes”) issued to BCV III and BCV IV on February 9, 2004 in the original principal amount of $184,078.10 and $1,168,072.30, respectively (the “Debt Conversion”), and (iii) grant registration rights to the Investors with respect to the Series I Preferred Stock purchased pursuant to the Series I SPA;

WHEREAS, the written consent of the Company and the holders of at least (i) 51% of the outstanding shares of the Company’s Series A Preferred Stock, (ii) 80% of the outstanding shares of Series B Preferred Stock, (iii) 80% of the outstanding shares of Series C Preferred Stock, (iv) 80% of the outstanding shares of Series E Preferred Stock, (v) 80% of the outstanding shares of Series F Preferred Stock, and (vi) 70% of the aggregate amount of the shares of Series H Preferred Stock that would be issued upon conversion of the Series H Notes (as defined in the Series H Purchase Agreement) as if converted on the date of such consent, is necessary to waive the Participation Rights (and notice of such rights) on behalf of all stockholders entitled to such rights;

WHEREAS, the written consent of the Company and the holders of at least (i) a majority of the shares of Series A Preferred Stock, (ii) a majority of the shares of Series B Preferred Stock, and (iii) 67% of the Registrable Securities (as defined in the Purchase Agreements), including at least two Institutional Holders (as defined in the Purchase Agreements) is necessary to amend Section 8 of the Purchase Agreements; and

WHEREAS, the Requisite Shareholders hold a sufficient number of shares of each series of Preferred Stock necessary to (i) waive the Participation Rights on behalf of all stockholders with respect to both the Cash Financing and the Debt Conversion, and (ii) amend the Purchase Agreements and the terms of the Registration Rights provided for therein.

NOW, THEREFORE, the Company and the undersigned Requisite Shareholders hereby agree as follows:

1. Amendment of Registration Rights Under the Purchase Agreements.

1.1 The Series A Purchase Agreement. Effective as of the Closing, Section 8 of the Series A Purchase Agreement is hereby amended by the deletion thereof in its entirety and the insertion in the place thereof the text of Section 8 in its entirety of the Series I SPA. The defined terms contained in such Section 8 of the Series I SPA shall be used in Section 8 of the Series A Purchase Agreement, as amended hereby, as so defined in the Series I SPA. Section 8 of the Series A Purchase Agreement, as amended hereby, and any defined terms used therein, shall only be amended by written approval by the Company and a majority of the holders of the Company’s Series A Preferred Stock provided, any such amendment shall also be approved as provided in Section 9.5 of the Series I SPA.

1.2 The Series B Purchase Agreement. Effective as of the Closing, Section 8 of the Series B Purchase Agreement is hereby amended by the deletion thereof in its entirety and the insertion in the place thereof the text of Section 8 in its entirety of the Series I SPA. The defined terms contained in such Section 8 of the Series I SPA shall be used in Section 8 of the Series B Purchase Agreement, as amended hereby, as so defined in the Series I SPA. Section 8 of the Series B Purchase Agreement, as amended hereby, and any defined terms used therein, shall only be amended by written approval by the Company and a majority of the holders of the Company’s Series B Preferred Stock provided, any such amendment shall also be approved as provided in Section 9.5 of the Series I SPA.

1.3 The Series C Purchase Agreement, the Series E Purchase Agreement, the Series F Purchase Agreement and the Series H Purchase Agreement. Effective as of the Closing, Section 8 of each of the Series C Purchase Agreement, the Series E Purchase Agreement, the Series F Purchase Agreement, and the Series H Purchase Agreement (the “Series C, E, F and H Purchase Agreements”) is hereby amended by the deletion thereof in its entirety and the insertion in the place thereof the text of Section 8 in it entirety of the Series I SPA. The defined terms contained in such Section 8 of the Series I SPA shall be used in Section 8 of each of the Series C, E, F, and H Purchase Agreements, as amended hereby, as so defined in the Series I SPA. Section 8 of each of the Series C, E, F, and H Purchase Agreements, as amended hereby, and any defined terms used therein, shall only be approved as provided in Section 9.5 of the Series I SPA.

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2. Amendment of Redemption Rights. By signing this Amendment and Waiver, W Capital Partners Mustang, L.P. hereby consents to the deletion of Section 7 of the Company’s Certificate of Incorporation, as amended, in its entirety (including, without limitation, the redemption rights provided for therein).

3. Waiver of Participation Rights. By signing this Amendment and Waiver, the Company and the Requisite Shareholders hereby waive the Participation Rights to participate in the Cash Financing and the Debt Conversion, and waive notice of such Participation Rights, on behalf of all stockholders entitled to such rights.

4. Acknowledgment of Interested Directors. Each of the Requisite Shareholders acknowledges that they (a) understand the interests of each of the Company’s Board of Directors in the consummation of the Cash Financing and the Debt Conversion and (b) consider the terms of the Cash Financing and the Debt Conversion to be fair to the Company’s security holders.

5. Acknowledgment of Information. Each of the Requisite Shareholders acknowledges that they have had the opportunity to read, understand, review and consider all of the provisions of this Amendment and Waiver and the Series I SPA and that they have had the opportunity to discuss such documents with legal counsel of their own choosing and that they have had the opportunity to ask questions of the Company.

6. Miscellaneous. Except to the extent specifically modified hereby, the provisions of the Purchase Agreements shall remain unmodified, and the Purchase Agreements as amended hereby are confirmed as being in full force and effect. This agreement may be executed in any number of counterparts which together shall constitute a single instrument and shall be governed by and construed in accordance with the domestic substantive laws of The Commonwealth of Massachusetts.

7. Definitions. Reference is made to (i) the Series A Preferred Stock and Warrant Purchase Agreement dated April 30, 1993, as amended on November 2, 1994, September 30, 1996, November 27, 1996 and January 28, 1998, among the Company and the Investors party thereto (as amended, the “Series A Purchase Agreement”), (ii) the Series B Convertible Preferred Stock Purchase Agreement dated November 2, 1994, as amended on September 30, 1996, November 27, 1996 and January 28, 1998, among the Company and the Investors party thereto (the “Series B Purchase Agreement”), (iii) the Series C Convertible Preferred Stock Purchase Agreement dated September 30, 1996, as amended on November 27, 1996 and January 28, 1998, among the Company and the Investors party thereto (the “Series C Purchase Agreement”), (iv) the Series E Convertible Stock Purchase Agreement dated January 28, 1998 among the Company and the Investors party thereto (the “Series E Purchase Agreement”), (v) the Series F Convertible Stock Purchase Agreement dated January 28, 1998 among the Company and the Investor party thereto (the “Series F Purchase Agreement”), and (vi) the Note Purchase Agreement dated February 9, 2004 among the Company and the Investors party thereto (the “Series H Purchase Agreement”) (collectively, the “Purchase Agreements”). The Series C Purchase Agreement, the Series E Purchase Agreement, the Series F Purchase Agreement, and the Series H Purchase Agreement are collectively referred to herein as the “Series C, E, F, and H Purchase Agreements.” Terms defined in the Purchase Agreements, as amended hereby, and not otherwise defined herein are used herein as so defined.

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8. Effectiveness. This Amendment and Wavier shall become a binding agreement when the Company has received copies of this Amendment and Waiver executed by the Company and the holders of at least (i) 51% of the outstanding shares of Series A Preferred Stock, (ii) 80% of the outstanding shares of Series B Preferred Stock (iii) 80% of the outstanding shares of Series C Preferred Stock, (iv) 80% of the outstanding shares of Series E Preferred Stock, (v) 80% of the outstanding shares of Series F Preferred Stock, and (vi) 70% of the aggregate amount of the shares of Series H Preferred Stock that would be issued upon conversion of the Series H Notes.

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IN WITNESS WHEREOF, the undersigned parties have executed this Amendment and Waiver as an instrument under seal.

FIDELITY VENTURES LTD.

Fidelity Capital Associates, Inc., Its Managing General Partner

FIDELITY INVESTORS LIMITED PARTNERSHIP

By:   Northern Neck Investors Corporation, Its General Partner

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FMR LLC

BOSTON CAPITAL VENTURES III, LIMITED PARTNERSHIP

BOSTON CAPITAL VENTURES IV, LIMITED PARTNERSHIP

MASSACHUSETTS CAPITAL RESOURCE COMPANY

W CAPITAL PARTNERS MUSTANG, L.P.

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