UNIT APPRECIATION RIGHTS AGREEMENT UNDER THE STONEMOR PARTNERS L.P. LONG-TERM INCENTIVE PLAN

Exhibit 10.1

UNIT APPRECIATION RIGHTS AGREEMENT

UNDER THE

STONEMOR PARTNERS L.P. LONG-TERM INCENTIVE PLAN

This Key Employee Unit Appreciation Rights Agreement (the “Agreement”) entered into as of December 16, 2009, (the “Agreement Date”), by and between StoneMor GP LLC (the “Company”), the general partner of and acting on behalf of StoneMor Partners L.P., a Delaware limited partnership (the “Partnership”), and                                 , a key employee of the Company or its Affiliates (the “Participant”).

BACKGROUND:

In order to make certain awards to key employees, directors and consultants of the Company and its Affiliates, the Company maintains on behalf of the Partnership the StoneMor Partners L.P. Long-Term Incentive Plan (the “Plan”). The Plan is administered by the Compensation Committee (the “Committee”) of the Board of Directors (“Board”) of the Company. The Committee has determined to grant to the Participant, pursuant to the terms and conditions of the Plan, an award (the “Award”) of Unit Appreciation Rights Agreement (also called “UARS”), which entitles the holder to receive, in whole Common Units of the Partnership (“Common Units”) the excess of the Fair Market Value of a Common Unit on the exercise date over the exercise base price established for the UARS, subject to the terms and conditions contained herein. The exercise base price for the UAR is intended to equal to Fair Market Value of a Common Unit on the Date of Grant (as defined herein). The Participant has determined to accept such Award. Any initially capitalized terms and phrases used in this Agreement, but not otherwise defined herein, shall have the respective meanings ascribed to them in the Plan.

NOW, THEREFORE, the Company, acting on behalf of the Partnership, and the Participant, each intending to be legally bound hereby, agree as follows:

ARTICLE I

AWARD OF UARS

1.1 Grant of UARS and Vesting. The Participant is hereby granted the following UARS under the Plan and the following terms shall have the following respective meanings as used hereafter in this Agreement:

UARS vest at a percentage rate which is equal to a fraction the numerator of which is the number of calendar months which have elapsed since December 16, 2009 and the denominator of which is 48, subject to forfeiture contained in Section 1.4 hereof.

All of the UARS shall automatically vest upon a Change of Control (as defined in the Plan), notwithstanding that the UARS have not otherwise vested, provided that, at the time of

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the Change of Control, the Participant is then employed by the Company or any of its Affiliates. All of the UARS shall automatically vest upon retirement at or after age 60 of a Participant who has at least 25 years of service with the Company or any of its predecessor’s companies (as determined by the Committee).

The term “permanent disability”, as used in Section 1.4, shall refer to a “disability” as defined in Regulation 1.409A-3(i)(4)(i) and any successor guidance under the Code. All decisions as to whether UARS have fully vested or as to whether a Participant has suffered a “permanent disability” shall be made by the Committee and its decision shall be final, binding and conclusive in the absence of clear and convincing evidence that such decision was not made in good faith.

1.2 Exercise of UARS.

(a) UARS may not be exercised prior to vesting, and only to the extent vested, and exercise is subject to all the terms and conditions of the Plan, including, but not limited to, the conditions set forth in Section 1.2(c) hereof. UARS which have vested may be exercised by giving written exercise notice to the Company on the form supplied by the Company. UARS are not deemed exercised until the Participant has paid or made suitable arrangements to pay all required tax withholding under Section 2.3 hereof, which will include (i) all foreign, federal, state and local income tax withholding required to be withheld by the Company in connection with the exercise of the UARS and (ii) the employee’s portion of other foreign, federal, state and local payroll and other taxes due in connection with the exercise of the UARS.

(b) Upon proper exercise of UARS, the Participant will be entitled to receive, with respect to the UARS which are exercised, that number of whole Common Units that is closest in Fair Market Value (but does not exceed) the excess (if any) of (i) the Fair Market Value of the Common Units on the last trading date preceding the receipt by the Company of the written exercise notice (or if there is no trading in the Common Units on such date, on the next preceding date on which there was trading) as reported in The Wall Street Journal (or other reporting service approved by the Committee) over (ii) the Exercise Base Price For Each of the UARS contained in Section 1.1. No fractional Common Units shall be issued; instead, cash shall be distributed equal in Fair Market Value to the value of a whole Common Unit multiplied by the fraction. In the event Common Units are not publicly traded at the time a determination of Fair Market Value is required to be made herein, the determination of Fair Market Value shall be made in good faith by the Committee. The Committee’s determination of Fair Market Value shall be final, binding and conclusive in absence of clear and convincing evidence that such decision was not made in good faith.

(c) The Plan provides as follows: “The Committee may refuse to issue or transfer any Units or other consideration under an Award if, in its sole discretion, it determines that the issuance or transfer of such Units or such other consideration might violate any applicable law or regulation, the rules of the principal securities exchange on which the Units are then traded, or entitle the Partnership or an Affiliate to recover the same under Section 16(b) of the Exchange Act, and any payment tendered to the Company by a Participant, other holder or beneficiary in connection with the exercise of such Award shall be promptly refunded to the relevant Participant, holder or beneficiary.” The exercise of UARS may be subject to approval by the limited partners of the Partnership as required by the listing rules of The Nasdaq Stock

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Market, Inc. In no event may a UAR be exercised in violation of the Second Amended and Restated Agreement of Limited Partnership of the Partnership.

1.3 Exercise Term. Subject to Section 1.4 hereof, UARS’ may not be exercised more than five (5) years after the Date of Grant contained in Section 1.1.

1.4 Forfeiture of UARS Upon Termination of Employment. In the event of the termination of the employment of the Participant (whether voluntary or involuntary and regardless of the reason for the termination) with the Company or its Affiliates, all UARS (whether or not vested) shall be deemed to be automatically forfeited, unless the Participant’s employment is on that date transferred to the Company or another Affiliate. If a Participant’s employment is with an Affiliate and that entity ceases to be an Affiliate, the Participant’s employment will be deemed to have terminated when the entity ceases to be an Affiliate unless the Participant transfers employment to the Company or its remaining Affiliates. Notwithstanding the foregoing, in the event of the termination of the Participant’s employment with the Company or any of its Affiliates by reason of (a) a Change of Control (as defined in the Plan); (b) the death of the Participant; (c) the permanent disability of the Participant (as determined by the Committee); or (d) the retirement of the Participant at such age as the Committee shall approve, no forfeiture shall apply.

1.5 No Rights as Holder of Common Units. The Participant is not entitled to the rights of a holder of Common Units (including, but not limited to, the right to receive distributions on Common Units) until certificates representing the Common Units have been delivered to the Participant after proper exercise of the UARS.

ARTICLE II

GENERAL PROVISIONS

2.1 No Right Of Continued Employment. The receipt of this Award does not give the Participant, and nothing in the Plan or in this Agreement shall confer upon the Participant, any right to continue in the employment of the Company or any of its Affiliates. Nothing in the Plan or in this Agreement shall affect any right which the Company or any of its Affiliates may have to terminate the employment of the Participant.

2.2 No Rights As A Limited Partner. Neither the Participant nor any other person shall be entitled to the privileges of ownership of Common Units of the Partnership, limited partnership interests in the Partnership, or otherwise have any rights as a limited partner, by reason of the award of the UARS covered by this Agreement.

2.3 Tax Withholding. The Participant is responsible to pay to the Company all required tax withholding, whether foreign, federal, state or local in connection with the exercise of the UARS.

2.4 Administration. Pursuant to the Plan, the Committee is vested with conclusive authority to interpret and construe the Plan, to adopt rules and regulations for carrying out the Plan, and to make determinations with respect to all matters relating to this Agreement, the Plan and awards made pursuant thereto. The authority to manage and control the operation and administration of this Agreement shall be likewise vested in the Committee, and the Committee shall have all powers with respect to this Agreement as it has with respect to the Plan. Any

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interpretation of this Agreement by the Committee, and any decision made by the Committee with respect to this Agreement, shall be final and binding.

2.5 Effect of Plan; Construction. The entire text of the Plan is expressly incorporated herein by this reference and so forms a part of this Agreement. In the event of any inconsistency or discrepancy between the provisions of this Agreement and the terms and conditions of the Plan under which the UARS are granted, the provisions of the Plan shall govern and prevail. The UARS and this Agreement are each subject in all respects to, and the Company and the Participant each hereby agree to be bound by, all of the terms and conditions of the Plan, as the same may have been amended from time to time in accordance with its terms; provided, however, that no such amendment shall deprive the Participant, without the Participant’s consent, of any rights earned or otherwise due to the Participant hereunder.

2.6 Amendment, Supplement or Waiver. This Agreement shall not be amended, supplemented, or waived in whole or in part, except by an instrument in writing executed by the parties to this Agreement.

2.7 Captions. The captions at the beginning of each of the numbered Sections and Articles herein are for reference purposes only and will have no legal force or effect. Such captions will not be considered a part of this Agreement for purposes of interpreting, construing or applying this Agreement and will not define, limit, extend, explain or describe the scope or extent of this Agreement or any of its terms and conditions.

2.8 Governing Law. THE VALIDITY, CONSTRUCTION, INTERPRETATION AND EFFECT OF THIS AGREEMENT SHALL EXCLUSIVELY BE GOVERNED BY AND DETERMINED IN ACCORDANCE WITH THE LAWS OF THE COMMONWEALTH OF PENNSYLVANIA (WITHOUT GIVING EFFECT TO THE CONFLICTS OF LAW PRINCIPLES THEREOF), EXCEPT TO THE EXTENT PREEMPTED BY FEDERAL LAW.

2.9 Notices. All notices, requests and demands to or upon the respective parties hereto to be effective shall be in writing, sent by facsimile, by overnight courier or by registered or certified mail, postage prepaid and return receipt requested, or hand-delivered by the Participant and acknowledged in writing by the Company. Notices to the Company shall be deemed to have been duly given or made upon actual receipt by the Company. Such communications shall be addressed and directed to the parties listed below (except where this Agreement expressly provides that it be directed to another) as follows, or to such other address or recipient for a party as may be hereafter notified by such party hereunder:

2.10 Severability. If any provision hereof is found by a court of competent jurisdiction to be prohibited or unenforceable, it shall, as to such jurisdiction, be ineffective only to the extent of such prohibition or unenforceability, and such prohibition or unenforceability shall not

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invalidate the balance of such provision to the extent it is not prohibited or unenforceable, nor invalidate the other provisions hereof.

2.11 Entire Agreement; Counterparts; Construction. This Agreement constitutes the entire understanding and supersedes any and all other agreements, oral or written, between the parties hereto, in respect of the subject matter of this Agreement, and embodies the entire understanding of the parties with respect to the subject matter hereof. This Agreement may be executed in one or more counterparts, each of which shall be deemed an original against any party whose signature appears thereon. The rule of construction that ambiguities in a document are construed against the draftsperson shall not apply to this Agreement.

2.12 Binding Agreement. The terms and conditions of this Agreement shall be binding upon the estate, heirs, beneficiaries and other representatives of the Participant to the same extent that said terms and conditions are binding upon the Participant.

2.13 Arbitration. Any dispute or disagreement with respect to any portion of this Agreement or its validity, construction, meaning, performance, or Participant’s rights hereunder shall be settled by arbitration, conducted in Philadelphia, Pennsylvania, in accordance with the Commercial Arbitration Rules of the American Arbitration Association or its successor, as amended from time to time. However, prior to submission to arbitration the Participant will attempt to resolve any disputes or disagreements with the Partnership over this Agreement amicably and informally, in good faith, for a period not to exceed two weeks. Thereafter, the dispute or disagreement will be submitted to arbitration. At any time prior to a decision from the arbitrator(s) being rendered, the Participant and the Partnership may resolve the dispute by settlement. The Participant and the Partnership shall equally share the costs charged by the American Arbitration Association or its successor, but the Participant and the Partnership shall otherwise be solely responsible for their own respective counsel fees and expenses. The decision of the arbitrator(s) shall be made in writing, setting forth the award, the reasons for the decision and award and shall be binding and conclusive on the Participant and the Partnership. Further, neither Participant nor the Partnership shall appeal any such award. Judgment of a court of competent jurisdiction may be entered upon the award and may be enforced as such in accordance with the provisions of the award. THE PARTICIPANT HEREBY WAIVES ANY RIGHT TO A JURY TRIAL.

IN WITNESS WHEREOF, the parties hereto, intending to be legally bound hereby, have executed this Agreement as of the day first above written.

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The Participant hereby acknowledges receipt of a copy of the foregoing Unit Appreciation Rights Agreement and the Plan, and having read them, hereby signifies his or her understanding of, and his or her agreement with, their terms and conditions. The Participant hereby accepts this Agreement in full satisfaction of any previous written or verbal promises made to him or her by the Partnership or the Company or any of its other Affiliates with respect to Awards under the Plan, but does not affect outstanding Awards.

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