NON-QUALIFIED STOCK OPTION AGREEMENT FOR DIRECTORS UNDER THE FOURTH AMENDED AND RESTATED ANSYS, INC. 1996 STOCK OPTION AND GRANT PLAN

Exhibit 10.4

NON-QUALIFIED STOCK OPTION AGREEMENT

FOR DIRECTORS

UNDER THE FOURTH AMENDED AND RESTATED ANSYS, INC.

1996 STOCK OPTION AND GRANT PLAN

Name of Optionee:                                                              

No. of Option Shares:                     

Option Exercise Price per Share: $                     [FMV on Grant Date]

Grant Date:                                                              

Expiration Date:                                          [Seven years after Grant Date]

Pursuant to the Fourth Amended and Restated ANSYS, Inc. 1996 Stock Option and Grant Plan, as amended through the date hereof (the “Plan”), ANSYS, Inc. (the “Company”) hereby grants to the Optionee named above, who is the Chairman of the Board of Directors (provided he or she is not an officer of the Company) or a non-affiliate Independent Director (as defined in the Plan), an option (the “Stock Option”) to purchase on or prior to the Expiration Date specified above, all or part of the number of shares of Common Stock, par value $0.01 per share (the “Stock”), of the Company specified above at the Option Exercise Price per Share specified above subject to the terms and conditions set forth herein and in the Plan. This Stock Option is not intended to be an “incentive stock option” under Section 422 of the Internal Revenue Code of 1986, as amended.

1. Exercisability Schedule. No portion of this Stock Option may be exercised until such portion shall have become exercisable. Except as set forth below, and subject to the discretion of the Committee (as described in Section 2 of the Plan) to accelerate the exercisability schedule hereunder, this Stock Option shall be exercisable with respect to the following number of Option Shares on the dates indicated:

Once exercisable, this Stock Option shall continue to be exercisable at any time or times prior to the close of business on the Expiration Date, subject to the provisions hereof and of the Plan.

2. Manner of Exercise.

(a) The Optionee may exercise this Stock Option only in the following manner: from time to time on or prior to the Expiration Date of this Stock Option, the Optionee may elect to purchase some or all of the Option Shares with respect to which this Stock Option has vested via the broker of his or her choice (which may include the Company’s dedicated on-line broker).

(i) Payment of the purchase price for the Option Shares, as well as payment for any applicable taxes withheld by the Company, is coordinated through the chosen broker and then wired directly to the Company upon settlement.

(ii) The transfer to the Optionee on the records of the Company or of the transfer agent of the Option Shares will be contingent upon the Company’s receipt from the Optionee of full payment for the Option Shares, as set forth above and any agreement, statement or other evidence that the Company may require to satisfy itself that the issuance of Stock to be purchased pursuant to the exercise of Stock Options under the Plan and any subsequent resale of the shares of Stock will be in compliance with applicable laws and regulations.

(b) The shares of Stock purchased upon exercise of this Stock Option shall be transferred to the Optionee on the records of the Company or of the transfer agent upon compliance to the satisfaction of the Committee with all requirements under applicable laws or regulations in connection with such issuance and with the requirements hereof and of the Plan. The determination of the Committee as to such compliance shall be final and binding on the Optionee. The Optionee shall not be deemed to be the holder of, or to have any of the rights of a holder with respect to, any shares of Stock subject to this Stock Option unless and until this Stock Option shall have been exercised pursuant to the terms hereof, the Company or the transfer agent shall have transferred the shares to the Optionee, and the Optionee’s name shall have been entered as the stockholder of record on the books of the Company. Thereupon, the Optionee shall have full voting, dividend and other ownership rights with respect to such shares of Stock.

(c) The minimum number of shares with respect to which this Stock Option may be exercised at any one time shall be 100 shares, unless the number of shares with respect to which this Stock Option is being exercised is the total number of shares subject to exercise under this Stock Option at the time.

(d) Notwithstanding any other provision hereof or of the Plan, no portion of this Stock Option shall be exercisable after the Expiration Date hereof.

3. Termination as Director. Subject to Section 4 below, if the Optionee ceases to be a Director of the Company for any reason, this Stock Option shall no longer vest or become exercisable with respect to any Option Shares not vested.

(a) Termination by Reason of Death. If the Optionee ceases to be a Director by reason of the Optionee’s death, any portion of this Stock Option exercisable on such date may be exercised by his or her legal representative or legatee for a period of 12 months from the date of death or until the Expiration Date, if earlier.

(b) Termination by Reason of Disability. If the Optionee ceases to be a Director by reason of the Optionee’s disability (as defined in Section 422(c)(6) of the Code), any portion of this Stock Option exercisable on such date may be exercised for a period of six months from the date of termination or until the Expiration Date, if earlier.

(c) Termination for Cause. If the Optionee is removed for cause as a Director of the Company pursuant to the terms of the Company’s By-laws and Restated Certificate of Incorporation (the “Certificate of Incorporation”), any portion of this Stock Option outstanding on such date shall terminate immediately and be of no further force and effect as of the date of such removal. For purposes hereof, “cause” shall have the meaning set forth in the Company’s Certificate of Incorporation.

(d) Other Termination. If the Optionee ceases to be a Director for any reason other than the Optionee’s death or disability, any portion of this Stock Option exercisable on such date may be exercised for a period of 60 days from the date of termination or until the Expiration Date, if earlier.

4. Effect of a Transaction. In the case of a Transaction (as defined in Section 3 of the Plan), this Stock Option shall be subject to Section 3(c) of the Plan. In addition, notwithstanding anything herein to the contrary, in the event that this Stock Option is assumed in the sole discretion of the parties to a Transaction or is continued by the Company and thereafter remains in effect following such Transaction, then this Stock Option shall be deemed vested and exercisable in full upon the date on which the Optionee ceases to be a member of the Board if, at or in connection with the closing of the Transaction or within 18 months following such Transaction, (i) the Optionee stands for re-election and is not re-elected to the Board, (ii) the Optionee is removed from his position as a Director by the Board or the stockholder or stockholders of the Company, or (iii) the Optionee is required or requested by the Board or the acquirer to resign from the Board, including any resignation contemplated by or in connection with the terms of such Transaction.

5. Incorporation of Plan. Notwithstanding anything herein to the contrary, this Stock Option shall be subject to and governed by all the terms and conditions of the Plan, including the powers of the Committee set forth in Section 2(b) of the Plan. Capitalized terms in this Agreement shall have the meaning specified in the Plan, unless a different meaning is specified herein.

6. Transferability. This Agreement is personal to the Optionee, is non-assignable and is not transferable by Optionee in any manner, by operation of law or otherwise, other than by will or the laws of descent and distribution.

2

This Stock Option is exercisable, during the Optionee’s lifetime, only by the Optionee, and thereafter, only by the Optionee’s legal representative, beneficiary or legatee. The Optionee may designate a beneficiary by providing written notice of the name of such beneficiary to the Company, and may revoke or change such designation at any time by filing written notice of revocation or change with the Company.

7. Tax Withholding. In the case of a Director who is also an employee, the Optionee shall, not later than the date as of which the exercise of this Stock Option becomes a taxable event for Federal income tax purposes, pay to the Company or make arrangements satisfactory to the Committee for payment of any Federal, state, and local taxes required by law to be withheld on account of such taxable event, in accordance with Section 2 hereof.

8. No Obligation to Continue as a Director. Neither the Plan nor this Stock Option confers upon the Optionee any rights with respect to continuance as a Director.

9. Notices. Notices hereunder shall be mailed or delivered to the Company at its principal place of business and shall be mailed or delivered to the Optionee at the address on file with the Company or, in either case, at such other address as one party may subsequently furnish to the other party in writing.

10. Amendment. Pursuant to Section 13 of the Plan, the Committee may at any time amend or cancel any outstanding portion of this Stock Option, but no such action may be taken that adversely affects the Optionee’s rights under this Agreement without the Optionee’s consent.

11. Severability. If any provision(s) of this Agreement shall be determined to be illegal or unenforceable, such determination shall in no manner affect the legality or enforceability of any other provision hereof.

12. Counterparts. For the convenience of the parties and to facilitate execution, this Agreement may be executed in two or more counterparts, each of which shall be deemed an original, but all of which shall constitute one and the same document.

The foregoing Agreement is hereby accepted and the terms and conditions thereof hereby agreed to by the undersigned.

3