EXHIBIT 10.1

ANSYS, INC.

SECOND AMENDED AND RESTATED

EMPLOYEE STOCK PURCHASE PLAN

The purpose of the ANSYS, Inc. Second Amended and Restated Employee Stock Purchase Plan (“the Plan”) is to provide eligible employees of ANSYS, Inc. (the “Company”) and each Designated Subsidiary (as defined in Section 12) with opportunities to purchase shares of the Company’s common stock, par value $.01 per share (the “Common Stock”). One Million Six Hundred Thousand (1,600,000) 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.

1. Administration. The Plan will be administered by the Company’s Board of Directors (the “Board”) or by the Compensation Committee of the Board or other committee appointed by the Board for such purpose. The Board or committee that administers the Plan is referred to herein as the “Administrator.” The Administrator has authority to make rules and regulations for the administration of the Plan, and its interpretations and decisions with regard thereto shall be final and conclusive. No member of the Board, any such committee or any other individual exercising administrative authority with respect to the Plan shall be liable for any action or determination with respect to the Plan or any option granted hereunder.

2. Offerings. The Company will make one or more offerings to eligible employees to purchase the Common Stock under the Plan (“Offerings”). Unless otherwise determined by the Administrator, an Offering will begin on the first business day occurring on or after each February 1 and August 1 and will end on the last business day occurring on or before the following July 31 and January 31, respectively. The Administrator may, in its discretion, choose an Offering period of six months or less for each of the Offerings and choose a different Offering period for each Offering.

3. Eligibility. All individuals classified as employees on the payroll records of the Company and each Designated Subsidiary (including employees who are also directors of the Company) are eligible to participate in any one or more of the Offerings under the Plan, provided that as of the first day of the applicable Offering (the “Offering Date”) they are customarily employed by the Company or

a Designated Subsidiary for more than twenty (20) hours a week. Notwithstanding any other provision herein, individuals who are not contemporaneously classified as employees of the Company or a Designated Subsidiary for purposes of the Company’s or a Designated Subsidiary’s payroll system are not considered to be eligible employees of the Company or a Designated Subsidiary and shall not be eligible to participate in the Plan. In the event such individuals are reclassified as employees of the Company or a Designated Subsidiary for any purpose, including without limitation, common law or statutory employees, by any action of any third party or as a result of any private action or administrative proceeding, such individuals shall notwithstanding such reclassification, remain ineligible to participate in the Plan.

4. Participation. An employee eligible on any Offering Date may participate in such Offering by submitting an enrollment form to his or her appropriate payroll location at least fifteen (15) business days before the Offering Date (or by such other deadline as shall be established by the Administrator for the Offering). The form will (a) state a whole percentage to be deducted from such employee’s Compensation (as defined in Section 12) per pay period, (b) authorize the purchase of Common Stock for such employee in each Offering in accordance with the terms of the Plan and (c) specify the exact name or names in which shares of Common Stock purchased for such employee are to be issued pursuant to Section 10. An employee who does not enroll in accordance with these procedures will be deemed to have waived the right to participate. Unless an employee files a new enrollment form or withdraws from the Plan, such employee’s deductions and purchases will continue at the same percentage of Compensation for future Offerings, provided such employee remains eligible. Notwithstanding the foregoing, participation in the Plan will neither be permitted nor be denied contrary to the requirements of the Code.

5. Employee Contributions. Each eligible employee may authorize payroll deductions at a minimum of one percent (1%) up to a maximum of ten percent (10%) of his or her Compensation for each pay period. The Company will maintain book accounts showing the amount of payroll deductions made by each participating employee for each Offering. No interest will accrue or be paid on payroll deductions.

6. Deduction Changes. Unless the Administrator provides otherwise, an employee may increase or decrease his or her payroll deduction during any Offering. An employee may also terminate his or her payroll deduction for the remainder of the Offering, either with or without withdrawing from the Offering under Section 7. To increase, reduce or terminate his or her payroll deduction (without withdrawing from the Offering), an employee must submit a new enrollment form at least fifteen (15) business days (or such shorter period as shall be established by the

Administrator) before the payroll date on which the change becomes effective. Subject to the requirements of Sections 4 and 5, an employee may either increase or decrease his or her payroll deduction with respect to the next Offering by filing a new enrollment form at least fifteen (15) business days before the next Offering Date (or by such other deadline as shall be established for the Offering).

7. Withdrawal. An employee may withdraw from participation in the Plan by delivering a written notice of withdrawal to his or her appropriate payroll location. The employee’s withdrawal will be effective as of the next business day. Following an employee’s withdrawal, the Company will promptly refund such employee’s entire account balance under the Plan (after payment for any Common Stock purchased before the effective date of withdrawal). Partial withdrawals are not permitted. The employee may not begin participation again during the remainder of the Offering, but may enroll in a subsequent Offering in accordance with Section 4.

8. Grant of Options. On each Offering Date, the Company will grant to each eligible employee who is then a participant in the Plan an option (“Option”) to purchase on the last day of such Offering (the “Exercise Date”), at the Option Price hereinafter provided for, (a) a number of shares of Common Stock determined by dividing such employee’s accumulated payroll deductions on such Exercise Date by the Option Price, or (b) such other lesser maximum number of shares of Common Stock as shall have been established by the Administrator in advance of an Offering Period; provided, however, that such Option and the maximum number of shares to be purchased shall be subject to the limitations set forth below. Subject to the limitations herein, each employee’s Option shall be exercisable only to the extent of such employee’s accumulated payroll deductions on the Exercise Date. The purchase price for each share purchased under such Option (the “Option Price”) will be 90% of the Fair Market Value of the Common Stock on the Offering Date or the Exercise Date, whichever is less.

Notwithstanding the foregoing, no employee may be granted an option hereunder if such employee, immediately after the option was granted, would be treated as owning stock possessing five percent (5%) or more of the total combined voting power or value of all classes of stock of the Company or any Parent or Subsidiary (as defined in Section 12). For purposes of the preceding sentence, the attribution rules of Section 424(d) of the Code shall apply in determining the stock ownership of an employee, and all stock which the employee has a contractual right to purchase shall be treated as stock owned by the employee. In addition, no employee may be granted an Option which permits his or her rights to purchase stock under the Plan, and any other employee stock purchase plan of the Company and its Parents and Subsidiaries, to accrue at a rate which exceeds $25,000 of the fair market value of such stock (determined on the option grant date or dates) for

each calendar year in which the Option is outstanding at any time. The purpose of the limitation in the preceding sentence is to comply with Section 423(b)(8) of the Code and shall be applied taking Options into account in the order in which they were granted.

9. Exercise of Option and Purchase of Shares. Each employee who continues to be a participant in the Plan on the Exercise Date shall be deemed to have exercised his or her Option on such date and shall acquire from the Company such number of whole shares of Common Stock reserved for the purpose of the Plan as his or her accumulated payroll deductions on such date will purchase at the Option Price, subject to any other limitations contained in the Plan. Any amount remaining in an employee’s account at the end of an Offering solely by reason of the inability to purchase a fractional share will be carried forward to the next Offering; any other balance remaining in an employee’s account at the end of an Offering will be refunded to the employee promptly.

10. Issuance of Certificates. Certificates or book entries representing shares of Common Stock purchased under the Plan may be issued only in the name of the employee, in the name of the employee and another person of legal age as joint tenants with rights of survivorship, or in the name of a broker authorized by the employee to be his or her nominee for such purpose.

11. Holding Period. Unless the Administrator provides otherwise, an employee may not sell, exchange, assign, encumber, alienate, transfer, pledge or otherwise dispose of any shares of Common Stock acquired on the Exercise Date at the end of an Offering until the one-year anniversary of such Exercise Date.

12. Definitions.

The term “Compensation” means the amount of total cash compensation, prior to salary reduction pursuant to either Section 125 or 401(k) of the Code, including base pay, overtime, commissions and bonuses, but excluding allowances and reimbursements for expenses such as relocation allowances or travel expenses, income or gains on the exercise of Company stock options, and similar items.

The term “Designated Subsidiary” means any present or future Subsidiary (as defined below) that has been designated by the Administrator to participate in the Plan. The Administrator may so designate any Subsidiary, or revoke any such designation, at any time and from time to time, either before or after the Plan is approved by the stockholders.

The term “Fair Market Value of the Common Stock” means (i) if the Common Stock is admitted to trading on a national securities exchange, the closing price

reported for the Common Stock on such exchange for such date or, if no sales were reported for such date, for the last date preceding such date for which a sale was reported, or (ii) if clause (i) does not apply but the Common Stock is admitted to quotation on the National Association of Securities Dealers Automated Quotation System (“NASDAQ”), the average of the highest bid and lowest asked prices of the Common Stock reported on NASDAQ for such date or, if no bid and asked prices were reported for such date, for the last day preceding such date for which such prices were reported.

The term “Parent” means a “parent corporation” with respect to the Company, as defined in Section 424(e) of the Code.

The term “Subsidiary” means a “subsidiary corporation” with respect to the Company, as defined in Section 424(f) of the Code.

13. Rights on Termination of Employment. If a participating employee’s employment terminates for any reason before the Exercise Date for any Offering, no payroll deduction will be taken from any pay due and owing to such employee and the balance in such employee’s account will be paid to such employee or, in the case of death, to such employee’s designated beneficiary as if such employee had withdrawn from the Plan under Section 7. An employee will be deemed to have terminated employment, for this purpose, if the corporation that employs such employee, having been a Designated Subsidiary, ceases to be a Subsidiary, or if such employee is transferred to any corporation other than the Company or a Designated Subsidiary. An employee will not be deemed to have terminated employment for this purpose if the employee is on an approved leave of absence for military service, sickness or any other purpose approved by the Company, if the employee’s right to reemployment is guaranteed by statute, by contract or under the policy pursuant to which that leave of absence was granted or if the Administrator otherwise so provides in writing.

14. Special Rules. Notwithstanding anything herein to the contrary, the Administrator may adopt special rules applicable to the employees of a particular Designated Subsidiary, whenever the Administrator determines that such rules are necessary or appropriate for the implementation of the Plan in a jurisdiction where such Designated Subsidiary has employees; provided that such rules are consistent with the requirements of Section 423(b) of the Code. Such special rules may include (by way of example, but not by way of limitation) the establishment of a method for employees of a given Designated Subsidiary to fund the purchase of shares other than by payroll deduction, if the payroll deduction method is prohibited by local law or is otherwise impracticable. Any special rules established pursuant to this Section 14 shall, to the extent possible, result in the employees subject to such rules having substantially the same rights as other participants in the Plan.

15. Optionees Not Stockholders. Neither the granting of an Option to an employee nor the deductions from his or her pay shall constitute such employee a holder of the shares of Common Stock covered by an Option under the Plan until such shares have been purchased by and issued to such employee.

16. Rights Not Transferable. Rights under the Plan are not transferable by a participating employee other than by will or the laws of descent and distribution, and are exercisable during the employee’s lifetime only by the employee.

17. Application of Funds. All funds received or held by the Company under the Plan may be combined with other corporate funds and may be used for any corporate purpose.

18. Adjustment in Case of Changes Affecting Common Stock. In the event of a subdivision of outstanding shares of Common Stock, the payment of a dividend in Common Stock, or any other similar change affecting the Common Stock, the number of shares approved for the Plan, the share limitation set forth in Section 8 and any other relevant limit under the Plan shall be proportionately adjusted to give proper effect to such event.

19. Amendment of the Plan. The Board may at any time, and from time to time, amend the Plan in any respect, except that without the approval, within twelve (12) months of such Board action, by the holders of a majority of the shares of stock of the Company present or represented and entitled to vote at a meeting of stockholders, no amendment shall be made increasing the number of shares approved for the Plan or making any other change that would require stockholder approval in order for the Plan, as amended, to qualify as an “employee stock purchase plan” under Section 423(b) of the Code.

20. Insufficient Shares. If the total number of shares of Common Stock that would otherwise be purchased on any Exercise Date plus the number of shares purchased under previous Offerings under the Plan exceeds the maximum number of shares issuable under the Plan, the shares then available shall be apportioned among participants in proportion to the amount of payroll deductions accumulated on behalf of each participant that would otherwise be used to purchase Common Stock on such Exercise Date.

21. Termination of the Plan. The Plan may be terminated at any time by the Board. Upon termination of the Plan, all amounts in the accounts of participating employees shall be promptly refunded.

22. Governmental Regulations. The Company’s obligation to sell and deliver Common Stock under the Plan is subject to obtaining all governmental approvals required in connection with the authorization, issuance, or sale of such stock.

23. Governing Law. The Plan shall be governed by Delaware law except to the extent that such law is preempted by federal law.

24. Issuance of Shares. Shares may be issued upon exercise of an Option from authorized but unissued Common Stock, from shares held in the treasury of the Company, or from any other proper source.

25. Tax Withholding. Participation in the Plan is subject to any required tax withholding on income of the participant in connection with the Plan. Each employee agrees, by entering the Plan, that the Company and its Subsidiaries shall have the right to deduct any such taxes from any payment of any kind otherwise due to the employee, including shares issuable under the Plan.

26. Notification Upon Sale of Shares. Each employee agrees, by entering the Plan, to give the Company prompt notice of any disposition of shares purchased under the Plan where such disposition occurs within two years after the date of grant of the Option pursuant to which such shares were purchased.

27. Effective Date and Approval of Stockholders. The Plan was originally effective on the first day of the Company’s initial public offering and was approved by the Company’s stockholders in 1996. The Plan was subsequently amended to add additional shares of Common Stock to the Plan, which amendment was approved by the Company’s stockholders on May 6, 2004. The Plan was amended and restated in 2007, which amendment and restatement was approved by the Board on July 26, 2007.