American Science & Engineering, Inc. 2005 Equity and Incentive Plan Restricted Stock Unit Award Agreement

Exhibit 10.31

[Participant’s Name]

American Science & Engineering, Inc.

2005 Equity and Incentive Plan

Restricted Stock Unit Award Agreement

American Science & Engineering, Inc.

829 Middlesex Turnpike

Billerica, Massachusetts 01821

The undersigned (i) acknowledges that he or she has been granted an award (the “Award”) of restricted stock units (“Units”) from American Science & Engineering, Inc. (the “Company”) under the 2005 Equity & Incentive Plan (the “Plan”) under which the undersigned may be issued shares (the “Shares”) of common stock of the Company (“Stock”), subject to the satisfaction of certain vesting conditions set forth below and in the Plan; (ii) further acknowledges receipt of a copy of the Plan as in effect on the date hereof; and (iii) agrees with the Company as follows:

1.                          Effective Date.  This agreement (the “Agreement”) shall take effect as of [Date], which is the date of grant of the Award.

2.                          Shares Subject to Award.  The Award covers [# of shares] Shares (in the aggregate, “Aggregate Shares”) of Stock.  The undersigned’s rights to the Shares are subject to the restrictions described in the Agreement and the Plan (which is incorporated herein by reference with the same effect as if set forth herein in full) in addition to such other restrictions, if any, as may be imposed by law.

3.                          Meaning of Certain Terms.  Except as otherwise expressly provided, all terms used herein shall have the same meaning as in the Plan.  The term “vest” as used herein with respect to the Award means the satisfaction of the performance goals with respect to a portion of the Award, except as provided under Paragraphs 8 and 9 below (on Retirement or death).

4.                          Nontransferability of Units.  The Units received by the undersigned pursuant to this Agreement shall not be sold, transferred, pledged, assigned or otherwise encumbered or disposed of except as provided below and in the Plan.

5.                          Forfeiture Risk.  If the undersigned ceases to be employed by the Company and its subsidiaries for any reason (except as provided for in Paragraph 8 and 9 below), any then outstanding and unvested Units received by the undersigned hereunder shall be automatically and immediately forfeited.

6.                          Vesting of Units.  The Award shall vest upon the achievement of performance goals of the Company, as more particularly described herein.  The performance goals are specified in Exhibit A attached to this Agreement.  As soon as practicable after the end of each applicable Fiscal Year, but in no event later than seventy-five days after the end of that Fiscal Year, the Compensation Committee (the “Committee”) of the Company’s Board of Directors shall certify in writing whether any of the FY20XX LTIP Goals (the “Goals”), set forth in Exhibit A, have been met and, if and to the extent so certified, the applicable portions of the Award will then vest in accordance with the terms outlined in Exhibit A.  Unless otherwise provided herein, the vesting date is the date on which the Committee certifies in writing that the Goals have been satisfied.  Except as otherwise provided in Paragraphs 8 and 9 and Exhibit A, no portion of the Award shall vest on an otherwise applicable vesting date unless the undersigned is then, and since the date of grant has continuously been, employed by the Company or its subsidiaries.  Any unvested portions of the Award will expire automatically on the undersigned’s last day of employment after giving effect to Paragraph 8 or 9 when applicable.  Distribution of Shares with respect to the vested portion of the Award shall be made as soon after the vesting date as administratively practicable provided that in no event shall distribution of the Shares with respect to the vested portion of the Award be made later than the end of the calendar year in which that portion of the Award becomes vested.

7.                          Change of Control. In the event of a Change in Control, in addition to the provisions of Section 10(f) of the Plan, the Committee may require that any amounts delivered, exchanged or otherwise paid in respect of outstanding and

then unvested Units be placed in escrow or otherwise made subject to such restrictions as the Committee deems appropriate to carry out the intent of the Plan.  References in this Agreement to the Shares or Units shall refer, mutatis mutandis, to any such restricted amounts. The term ‘Change in Control’ or ‘Change in Control of the Company’ shall mean the occurrence hereafter of any of the following:

(a)                      Any person, other than the Company or an Affiliate, becomes a beneficial owner (within the meaning of Rule 13d-3, as amended, as promulgated under the Securities Exchange Act of 1934, as amended), directly or indirectly, in one or a series of transactions, of securities representing more than fifty percent (50%) of the combined voting power of the Company’s then outstanding securities;

(b)                      The consummation of a merger or consolidation of the Company with any other Person, other than a merger or consolidation which would result in the voting securities of the Company outstanding immediately prior thereto continuing to represent (either by remaining outstanding or by being converted into voting securities of the surviving entity) more than fifty percent (50%) of the combined voting power of the voting securities of the Company or such surviving entity outstanding immediately after such merger or consolidation;

(c)                       The closing of a sale or other disposition by the Company of all or substantially all of the assets of the Company;

(d)                      Individuals who constitute the Board of Directors on the date hereof (“Incumbent Directors”) cease for any reason to constitute at least a majority of the board; provided, that any individual who becomes a member of the Board subsequent to the date hereof, whose election or nomination for election was approved by a vote of at least two-thirds of the Incumbent Directors shall be treated as an Incumbent Director unless he or she assumed office as a result of an actual or threatened election contest with respect to the election or removal of directors; or

(e)                       A complete liquidation or dissolution of the Company;

provided, in each case, that such event also constitutes a “change in control event” within the meaning of Treasury Regulation Section 1.409A-3(i)(5).

8.                          Vesting Upon Retirement.  If the undersigned retires on or before [Date], the end of the term of the Award (the “Term”), then Units reflecting the percentage of such Award that has been accrued (but not previously distributed in the form of Shares) by the Company on its books at the time of the undersigned’s retirement date shall immediately vest, and the remainder shall be automatically and immediately forfeited.  For purposes hereof “retire” and “retirement” means termination of employment at or after age 60 with an aggregate of five (5) full years of service. “Retirement” does not include termination for “cause” at or after the age of 60.  Payment will be made in accordance with the last sentence of Paragraph 6, as modified, where applicable, for compliance with Paragraph 15(b).

9.                          Vesting Upon Death.  If the undersigned’s employment is terminated before the end of the Term by reason of death, then Units reflecting the percentage of such Award that has been accrued (but not previously distributed in the form of Shares) by the Company on its books at the time of the undersigned’s death shall immediately vest, and the remainder shall be automatically and immediately forfeited.  Payment will be made in accordance with the last sentence of Paragraph 6.

10.                   Dividend Equivalents.  The undersigned will be granted Dividend Equivalents based on the dividends declared on the Stock of the Company during the period between the date the Award is granted and the date that the Shares are distributed or expire and, with respect to cash dividends, will receive payment of such Dividend Equivalents. “Dividend Equivalent Rights” mean a credit based on the number of Shares then credited to the undersigned under this Agreement, equivalent to the cash, stock or other property dividends on shares of Company common stock.  Any Dividend Equivalents will be distributed to the undersigned within thirty (30) calendar days following the date the dividend is credited by the stock transfer agent to holders of the Company’s Stock, provided that the Board may make an alternative distribution or arrangement if the dividend to Stock holders cannot be paid in this manner with respect to a particular dividend.

11.                   No Right To Employment.  The undersigned shall have no claim or right to be granted an Award.  Neither the Plan nor this Award shall be deemed to give the undersigned the right to continued employment or to limit the right of the Company or an Affiliate to discharge the undersigned at any time.

12.                   Data Privacy and Electronic Delivery.  By executing this Agreement, the undersigned: (i) authorizes the Company, its Affiliates, and any agent of the Company or its Affiliates administering the Plan or providing Plan

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recordkeeping services thereto, to disclose to the Company, its Affiliates or third-party service providers such information and data as may be deemed necessary or appropriate to facilitate the grant of Awards; (ii) waives any data privacy rights that the undersigned may have with respect to such information; and (iii) authorizes the Company, its Affiliates, and third-party service providers to store and transmit such information in electronic form.  The undersigned agrees that the Company, its Affiliates, and their agents may deliver electronically all documents relating to the Plan or this Award.

13.                   Cancellation and Rescission of Award.  In consideration of this Award the undersigned agrees that if the undersigned breaches his or her obligations under the terms of the American Science & Engineering Employee Representation, Rights in Data, and Non-Compete Agreement, then the Company may cancel, suspend, withhold, or otherwise limit or restrict (in whole or in part) the vesting of this Award.  If this Award vests prior to the occurrence or discovery by the Company of any such breach, then the Committee may rescind the vesting of this Award at any time within the two (2) year period after such vesting.  In the event of any rescission, the undersigned shall pay to the Company the amount of income recognized upon distribution of any Shares in satisfaction of the Award and any further gain upon sale of such Shares, in such manner and on such terms and conditions as may be required by the Committee, and the Company shall be entitled to set-off the amount of any such income against any amount that may be owed to the undersigned, except as Section 409A of the Internal Revenue Code of 1986 or other applicable law may prohibit such offset.

14.                   Impact of Restatement of Financial Statements Upon Award.  If any of the Company’s financial statements are required to be restated as a result of errors, omissions, or fraud, the Committee may (in its sole discretion, but acting in good faith) direct that the Company recover all or a portion of the amount of income recognized upon the distribution of Shares under this Award and any additional gain realized upon any sale of such Shares with respect to any fiscal year of the Company the financial results of which are negatively affected by such restatement. The amount to be recovered from the undersigned shall be determined based on the effect, if any, that the restated financial statements have on the calculation of the performance results used for Exhibit A.  For example, if the restated revenue or return on net assets would have resulted in a smaller portion of the Award vesting, the recovery from the individual would be based on the shares that would have been earned if the financial statements had reflected initially the restated numbers, provided that the Committee may instead determine a greater or lesser amount for recovery. The Committee may determine to recover different amounts from different participants or different classes of participants on such bases as it shall deem appropriate.  In no event shall the amount to be recovered by the Company be less than the amount required to be repaid or recovered as a matter of law. The Committee shall determine whether the Company shall effect any such recovery (i) by seeking repayment from the undersigned, (ii) by reducing (subject to applicable law and the terms and conditions of the applicable plan, program, or arrangement) the amount that would otherwise be payable to the undersigned under any compensatory plan, program, or arrangement maintained by the Company or any of its Affiliates, (iii) by withholding payment of future increases in compensation (including the payment of any discretionary bonus amount) or grants of compensatory awards that would otherwise have been made in accordance with the Company’s otherwise applicable compensation practices, or (iv) by any combination of the forgoing.  The foregoing recovery rights are in addition to, and not in substitution for, any other clawback policies that may be adopted from time to time, including any required by Federal law, such as under Section 304 of Sarbanes-Oxley Act of 2002 or the Dodd-Frank Wall Street Reform and Consumer Protection Act or by the listing standards of Nasdaq.  Accordingly, the terms and provisions of this Award shall be deemed automatically amended from time to time to assure compliance with the Dodd-Frank Act and other applicable laws and such rules and regulations as hereafter may be adopted and in effect.

15.                   Certain Tax Matters.

(a)                     The undersigned expressly acknowledges that the distribution of the Shares under the Award, and the payment of Dividend Equivalents with respect to such Shares, may give rise to “wages” subject to withholding.  The undersigned expressly acknowledges and agrees that the undersigned’s rights hereunder are subject to the prompt payment to the Company in cash (or by such other means as may be acceptable to the Company in its discretion, including, if the Committee so determines, by the delivery of previously acquired Stock or shares of Stock acquired hereunder or by the withholding of amounts from any payment hereunder) all taxes required to be withheld in connection with such award, vesting or payment.

(b)                     The Award is intended to be exempt from the requirements of Section 409A on account of the short-term deferral exclusion or alternatively, if it is determined that the exemption is not applicable, then it is intended to comply with the requirements of Section 409A and must be construed consistently with that section.  Notwithstanding anything in the Plan or this Grant Agreement to the contrary, for persons who are or become eligible for Retirement during the Term, if the Units vest in connection with the undersigned’s

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“separation from service” within the meaning of Section 409A, as determined by the Company), and if (x) the undersigned is then a “specified employee” within the meaning of Section 409A at the time of such separation from service (as determined by the Company, by which determination the undersigned agrees he or she is bound) and (y) the distribution of the Shares under with respect to the Units will result in the imposition of additional tax under Section 409A if distributed to the undersigned within the six month period following his or her separation from service, then the distribution under such accelerated RSUs will not be made until the earlier of (i) the date six months and one day following the date of his or her separation from service or (ii) the 10th day after his or her date of death. Neither the Company nor any participant will have the right to accelerate or defer the delivery of any payment except to the extent specifically permitted or required by Section 409A. In any event, the Company makes no representations or warranty and will have no liability to participants or any other person, if any provisions of or distributions under this Agreement are determined to constitute deferred compensation subject to Section 409A but not to satisfy the conditions of that section.

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