EXHIBIT 10.4

FIRST AMENDMENT

TO

ANSYS, INC.

EMPLOYEE STOCK PURCHASE PLAN

WHEREAS, the ANSYS, Inc. Employee Stock Purchase Plan (the “Plan”) was previously adopted by the Board of Directors and the stockholders of ANSYS, Inc. (the “Company”) and became effective on the consummation of the Company’s initial public offering in 1996;

WHEREAS, the Plan was adopted by the Board of Directors and the stockholders of the Company as an incentive to assist the Company in attracting and retaining key personnel and to align the interests of the participating employees with those of the Company’s stockholders;

WHEREAS, the Plan is intended to constitute an “employee stock purchase plan” within the meaning of Section 423(b) of the Internal Revenue Code of 1986, as amended, and shall be interpreted in accordance with that intent;

WHEREAS, the Plan provides that the total number of shares of the Company’s common stock, $.01 par value per share (the “Common Stock”), which may be issued pursuant the Plan shall not exceed an aggregate of 210,000 shares of Common Stock;

WHEREAS, the Board of Directors of the Company believes that the number of shares of Common Stock remaining available for issuance under the Plan has become insufficient for the Company’s current and anticipated future needs;

WHEREAS, Paragraph (r) of the Plan provides that the Board of Directors of the Company may amend the Plan at any time, subject to certain conditions set forth therein; and

WHEREAS, the Board of Directors of the Company has determined that it is in the best interests of the Company to amend the Plan to provide that an additional 190,000 shares of Common Stock be made available for issuance under the Plan.

NOW, THEREFORE:

1. Amendment of Plan. The first paragraph of the Plan is hereby amended and restated to provide in its entirety as follows:

The purpose of the ANSYS, Inc. Employee Stock Purchase Plan (“the Plan”) is to provide eligible employees of ANSYS, Inc. (the “Company”) and its subsidiaries with opportunities to purchase shares of the Company’s common stock, par value $.01 per share (the “Common Stock”). Four hundred thousand (400,000) shares of Common Stock in the aggregate have been approved and reserved for this purpose. The Plan is intended to constitute an “employee stock purchase plan” within the meaning of Section 423(b) of the Internal Revenue Code of 1986, as amended (the “Code”), and shall be interpreted in accordance with that intent.

2. Effective Date of Amendment. This First Amendment to the Plan shall become effective upon the date that it is adopted by the Board of Directors of the Company; provided, however, that this First Amendment shall be subject to the approval of the Company’s stockholders in accordance with applicable laws and regulations at an annual or special meeting held within twelve months of such effective date.

IN WITNESS WHEREOF, this First Amendment to the Plan has been adopted by the Board of Directors of the Company this 5th day of February, 2004, and approved by the Company’s stockholders at the Company’s Annual Meeting of Stockholders held on May 6, 2004.