Exhibit 4.1

EVEREST RE GROUP, LTD.

2003 NON-EMPLOYEE DIRECTOR EQUITY COMPENSATION PLAN

EVEREST RE GROUP, LTD.

2003 NON-EMPLOYEE DIRECTOR EQUITY COMPENSATION PLAN

Section 1. Establishment and Purpose

The Everest Re Group, Ltd. 2003 Non-Employee Directors Equity Compensation Plan (the “Plan”) has been established by Everest Re Group, Ltd., a Bermuda company (the “Company”), to promote the interests of the Company and its shareholders by enhancing the Company’s ability to attract and retain the services of experienced and knowledgeable directors and by encouraging such directors to acquire an increased proprietary interest in the Company through the ownership of Common Shares. The Common Shares can be acquired through grants of stock in lieu of cash-based retainer fees and through grants of Option Awards.

Section 2. Definitions

The following terms, used herein, shall have the meaning specified:

(a) “Award” means the Retainer Award or an Option Award granted to any Eligible Director under the Plan.

(b) “Award Date” means the date on which an Award under the Plan is granted.

(c) “Award Agreement” means an agreement described in Section 8 hereof entered into between the Company and a Participant, setting forth the terms and conditions applicable to the Award granted to the Participant.

(d) “Board” means the Board of Directors of the Company as it may be comprised from time to time.

(e) Unless otherwise defined in an Award Agreement, “Cause” shall mean any one of the following: (i) the willful engaging by the Participant in continuing or repeated conduct which is demonstrably and materially injurious to the Company or its affiliates, (ii) commission by the Participant of an act that involves theft, fraud or dishonesty (whether or not involving the Company, its affiliates or Participant’s duties at or relating to the Company or its affiliates), (iii) the Participant’s continuing or repeated material failure to abide by or comply with the internal policies or procedures of the Company or its affiliates (as may be applicable to Directors) or any non-compete or confidentiality agreement with the Company or its affiliates, or (iv) conviction of any crime that constitutes a felony (whether or not involving the Company, its affiliates or the Participant’s duties at or relating to the Company or its affiliates).

(f) “Change in Control” shall be as defined in Section 10.

(g) “Code” means the Internal Revenue Code of 1986, and any successor statute, and the regulations promulgated thereunder, as it or they may be amended from time to time.

(h) “Committee” means the Committee as defined in Section 12.

(i) “Common Shares” means common shares of the Company, par value $.01 per share, or any security of the Company issued in substitution, exchange or lieu thereof.

(j) “Date of Termination” means the last day on which a Participant serves as a Director.

(k) “Director” means a member of the Board.

(l) “Effective Date” means the Effective Date as defined in Section 12(e).

(m) “Eligible Director” means each Director who is not an Employee of the Company.

(n) “Employee” means officers and employees of the Company or a Subsidiary, and excludes directors who are not also officers or employees of the Company or a Subsidiary. “Employee” includes consultants and advisors that provide bona fide services (other than services as a director) to the Company or a Subsidiary, provided that such services are not in connection with the offer or sale of securities of the Company or a Subsidiary in a capital-raising transaction.

(o) “Exchange Act” means the Securities Exchange Act of 1934, and any successor statute, as it may be amended from time to time.

(p) “Exercise Price” means a purchase or exercise price established by the Committee at the time an Option is granted.

(q) “Fair Market Value” means, unless otherwise provided in the Award Agreement, the average of the highest and lowest sale price of Common Shares as reported on the Composite Transaction Tape of the New York Stock Exchange (or on such other exchange, if any, on which the Common Shares are traded) on the relevant date, or if no sale of Common Shares are reported for such date, the next preceding day for which there is a reported sale. If Common Shares are not traded on any such exchange, Fair Market Value shall be as determined in the Award Agreement, or as may be determined in good faith by the Committee. In no event, shall the Fair Market Value be less than the prevailing par value of a Common Share to be issued under the Plan.

(r) “Option” means a non-qualified stock option Award granted under the Plan that entitles the Participant, for a certain period of time, to purchase Common Shares at an Exercise Price established by the Committee.

(s) “Participant” means any Eligible Director who has been granted an Award pursuant to this Plan.

(t) “Plan Year” shall mean each calendar year, with the first Plan Year beginning on the Effective Date and ending on December 31, 2003.

(u) “Retainer Fee” means the annual compensation fee for services to be rendered as a Director to be paid to each Eligible Director as determined annually by the Board in its sole discretion. Such fees are to be paid in cash, or in stock at the election of each Eligible Director as provided in Section 5 of this Plan, on a quarterly basis (or other period as may be determined by the Board). Cash payments will become payable as of the last business day of the applicable Plan Year quarter. For Retainer Fees to be paid in the form of stock, the payment date shall be the first business day of the next following Plan Year quarter.

(v) “Section 16” means Section 16 of the Exchange Act, and any successor statutory provision, and the rules promulgated thereunder, as it or they may be amended from time to time.

(w) “Subsidiary” means any corporation in which the Company, directly or indirectly, controls 50% or more of the total combined voting power of all classes of such corporation’s common equity.

Section 3. Eligibility

Persons eligible for Awards under the Plan shall consist solely of Eligible Directors.

Section 4. Awards

The Eligible Directors shall be eligible to receive any of the types of Awards enumerated in Sections 5 or 6, either singly, in tandem or in combination with other types of Awards, as provided herein or as the Committee may in its sole discretion determine. Retainer Awards shall only be granted if the Eligible Director elects to waive cash payment of all or a portion of the applicable Retainer Fees.

Section 5. Retainer Awards

(a) For each Plan Year, each Director who is an Eligible Director on the first day of that Plan Year shall be entitled to elect to be granted a stock-based “Retainer Award” for the year in lieu of receiving all or a portion of the

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Retainer Fee in cash. The Retainer Award shall be in the form of Common Shares having a Fair Market Value (as determined on the last day of the applicable Plan Year quarter) equal to the Retainer Fee that would otherwise be paid in cash.

(b) If a Director becomes an Eligible Director during a Plan Year, on a date other than the first day of the Plan Year, he shall be entitled to elect to be granted a Retainer Award for the remainder of the year in lieu of receiving all or a portion of the applicable Retainer Fee. The Retainer Award shall be in the form of Common Shares having a Fair Market Value (as determined on the last day of the applicable Plan Year quarter) equal to the Retainer Fee, subject to a pro-rata reduction to reflect the portion of the Plan Year prior to the date on which he becomes an Eligible Director.

(c) Common Shares awarded under this subsection 5(a) shall be fully vested as of the date of grant.

Section 6. Discretionary Option Awards.

(a) Discretionary Option Awards. The Committee may at any time, and from time to time, in its sole discretion, grant an Eligible Director an Option Award (a “Discretionary Option Award”), which shall be subject to the terms and conditions set forth in subsections (b) and (c) below.

(b) Terms of Option Awards.

(1) An Option Award shall entitle the Director to purchase Common Shares at an Exercise Price equal to the greater of:  

(i) 100% of the Fair Market Value of Common Shares as of the Award Date; or (ii) the par value of a Common Share.

(2) Unless otherwise provided by the Committee, the Option Award granted to an Eligible Director shall become exercisable with respect to one-third of the shares covered by the Option on the first anniversary of the date of grant and with respect to an additional one-third of the shares covered by the Option on each subsequent anniversary; provided, however, that such portion of the Option shall become exercisable only if such Director’s Date of Termination does not occur prior to the foregoing vesting dates. Notwithstanding any provision of the Plan to the contrary, the foregoing vesting schedule shall be subject to acceleration in the event of the Participant’s death, disability (as may be determined by the Committee) or in the event of a Change in Control.

(3) An Option Award shall expire on the earlier of: (i) the ten-year anniversary of the Award Date (ii) the three-year anniversary of the Director’s Date of Termination if termination occurs due to the Director’s death or disability, (iii) the Date of Termination, if such termination of service occurs due to removal for Cause, or (iv) the one-year anniversary of the Director’s Date of Termination if the termination of service occurs for reasons other than as listed in subsections (ii), or (iii). No Option shall be exercisable following a Director’s Date of Termination except to the extent that the Option is exercisable prior to, or becomes exercisable as of, such Date of Termination.

(c) Payment of Option Exercise Price. The payment of the Exercise Price of an Option granted under this Section 6 shall be subject to the following:

(1) Subject to the following provisions of this subsection 6(c), the full Exercise Price for Common Shares purchased on the exercise of an Option shall be paid at the time of such exercise.

(2) The Exercise Price of Common Shares subject to the Option may be paid in cash. At the discretion of the Committee, the purchase price may also be paid by the tender, by actual delivery or by attestation, of Common Shares owned for at least six months by the holder of the Option (the value of such Common Shares shall be the Fair Market Value on the date of exercise), through a combination of Common Shares and cash, or through such other means as the Committee determines are consistent with the Plan’s purpose and subject to and in compliance with applicable law. No fractional Common Shares will be issued or accepted.

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Section 7. Common Shares and Other Share-Based Awards Available Under Plan

(a) The Common Shares which may be issued pursuant to an Award under the Plan may be shares currently authorized but unissued or currently held or subsequently acquired by the Company or its subsidiaries, including shares purchased in the open market or in private transactions.

(b) Subject to the adjustment provisions of Section 9 hereof, the maximum aggregate number of shares that may be delivered to Participants and their beneficiaries under the Plan shall be equal to 500,000 Common Shares and the maximum number of shares that may be granted to any one Eligible Director in a single calendar year shall be 10,000 shares pursuant to Option Awards and 5,000 shares pursuant to Retainer Awards.

(c) To the extent that any Common Shares covered by an Award are not delivered to a Participant or beneficiary because the Award is forfeited or canceled, or the Common Shares are not delivered because the Award is settled in cash or used to satisfy the applicable tax withholding obligation, such shares shall not be deemed to have been delivered for purposes of determining the maximum number of Common Shares available for delivery under the Plan and they shall again be available under the Plan.

(d) If the Exercise Price of any Option granted under the Plan is satisfied by tendering Common Shares to the Company (by either actual delivery or by attestation), only the number of Common Shares issued net of the Common Shares tendered shall be deemed delivered for purposes of determining the maximum number of Common Shares available for delivery under the Plan.

(e) For the purposes of computing the total number of Common Shares granted under the Plan, each Option shall be deemed to be the equivalent of the maximum number of Common Shares that may be issued upon exercise of the particular Option. Additional rules for determining the number of Common Shares granted under the Plan may be adopted by the Committee, as it deems necessary and appropriate.

(f) No fractional Common Shares shall be distributed under the Plan and, instead, the Fair Market Value of such fractional share shall be distributed in cash, with the Fair Market Value determined as of the date the fractional share would otherwise have been distributable. For purposes of the foregoing sentence, if more than one Award or type of Award under the Plan is to be distributed in Common Shares on a single date, such Common Shares shall be aggregated prior to determining the number of whole and fractional shares to be distributed.

Section 8. Award Agreements

Each Option Award under the Plan shall be evidenced by an Award Agreement setting forth the number of Common Shares subject to the Award and such other terms and conditions applicable to the Award, as determined by the Committee, not inconsistent with the terms of the Plan and applicable law. The Committee may, but need not require that the Participant sign a copy of such document. Such document is referred to as the Award Agreement regardless of whether any Participant signature is required. In the event that the Committee requires that the Participant execute and return the Award Agreement, no person shall have any rights under the Award unless and until the Participant to whom such Award shall have been granted shall have properly executed and delivered to the Company the Award Agreement; provided, however, the execution and delivery of such an Award Agreement shall not be a precondition to the granting of such Award. By executing the Award Agreement, or submitting an option exercise form (whether or not the Award Agreement required execution) a Participant shall be deemed to have accepted and consented to any action taken under the Plan by the Committee, the Board or their delegates.

(a) Award Agreements shall include the following terms:

(1) Non-assignability. Unless otherwise specifically provided for by the Committee, a provision that no Option, while vested or unvested, or any other Award, while unvested, be assignable or transferable except by will or by the laws of descent and distribution and that, during the lifetime of a Participant, the Award shall be exercised, if exercisable, only by such Participant or by his or her guardian or legal representative.

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(2) Termination of Services. A provision describing the treatment of an Award in the event of the death, disability or other termination of a Participant’s service with the Company, including but not limited to terms relating to the vesting, time for exercise, forfeiture or cancellation of an Award in such circumstances. Participants who terminate service prior to the satisfaction of applicable conditions and restrictions associated with their Award(s) may be entitled to such Award(s) as and to the extent determined by the Committee.

(3) Rights as a Shareholder. A provision that a Participant shall have no rights as a shareholder with respect to any Common Shares covered by an Award until the date the Participant becomes the holder of record. Except as provided in Section 9 hereof, no adjustment shall be made for dividends or other rights, unless the Award Agreement specifically requires such adjustment.

(4) Minimum Exercise. No Option may be exercised for less than the lesser of 50 Common Shares or the full number of shares of Common Shares for which the Option is then exercisable.

(b) Other Terms. Award Agreements may include such other terms as the Committee may determine are necessary and appropriate to effect an Award to the Participant, including, but not limited to, the term of the Award, vesting provisions, any requirements for continued service with the Company, any other restrictions or conditions (including performance requirements) on the Award and the method by which restrictions or conditions lapse, the effect on the Award of a change in control of the Company, the price, amount or value of Awards, and the terms, if any, pursuant to which a Participant may elect to defer the receipt of cash or Common Shares under an Award.

Section 9. Adjustment Provisions

(a) In the event of any change in the outstanding shares of Common Shares by reason of a stock dividend or split, recapitalization, merger or consolidation (whether or not the Company is a surviving corporation), reorganization, combination or exchange of Common Shares or other similar corporate changes or an extraordinary dividend paid in cash or property, the number of Common Shares (or other securities) then remaining subject to this Plan, and the maximum number of shares that may be issued annually to anyone pursuant to this Plan, including those that are then covered by outstanding Awards, shall (i) in the event of an increase in the number of outstanding shares, be proportionately increased and the price for each share then covered by an outstanding Award shall be proportionately reduced, and (ii) in the event of a reduction in the number of outstanding shares, be proportionately reduced and the price for each share then covered by an outstanding Award shall be proportionately increased.

(b) In the event the adjustments described in clauses (i) and (ii) of subsection (a) of this Section 9 are inadequate to ensure equitable treatment of any Award holder, then, to the extent permissible under applicable law, the Committee shall make any further adjustments as it deems necessary to ensure equitable treatment of any holder of an Award as the result of any transaction affecting the securities subject to the Plan or as is required or authorized under the terms of any applicable Award Agreement.

(c) The existence of the Plan and the Awards granted hereunder shall not affect or restrict in any way the right or power of the Board or the shareholders of the Company to make or authorize any adjustment, recapitalization, reorganization or other capital structure of its business, any merger or consolidation of the Company, any issue of bonds, debentures, preferred or prior preference stock ahead of or affecting the Common Shares or the rights thereof, the dissolution or liquidation of the Company or any sale or transfer of all or any part of its assets or business, or any other corporate act or proceeding.

Section 10. Change of Control

In the event of a “Change in Control” of the Company (defined below), in addition to any action required or authorized by the terms of an Award Agreement, the Committee may, in its sole discretion, recommend that the Board take any of the following actions as a result, or in anticipation, of any such event to assure fair and equitable treatment of Participants:

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(a) offer to purchase any outstanding Award made pursuant to this Plan from the holder for its equivalent cash value, as determined by the Committee, as of the date of the change of control; or

(b) make adjustments or modifications to outstanding Awards as the Committee deems appropriate to maintain and protect the rights and interests of Participants following such change of control.

Any such action approved by the Board shall be conclusive and binding on the Company and all Participants.

(c) For purposes of this Section, a “Change of Control” shall mean the occurrence of any of the following:

(1) A tender offer or exchange offer whereby the effect of such offer is to take over and control the affairs of the Company, and such offer is consummated for the ownership of securities of the Company representing twenty-five percent (25%) or more of the combined voting power of the Company’s then outstanding voting securities.

(2) The Company is merged or consolidated with another corporation and, as a result of such merger or consolidation, less than seventy-five percent (75%) of the outstanding voting securities of the surviving or resulting corporation shall then be owned in the aggregate by the former shareholders of the Company, other than affiliates within the meaning of the Exchange Act or any party to such merger or consolidation.

(3) The Company transfers substantially all of its assets to another corporation or entity that is not a wholly owned subsidiary of the Company.

(4) Any person (as such term is used in Sections 3(a)(9) and 13(d)(3) of the Exchange Act) is or becomes the beneficial owner, directly or indirectly, of securities of the Company representing twenty-five percent (25%) or more of the combined voting power of the Company’s then outstanding securities, and the effect of such ownership is to take over and control the affairs of the Company.

(5) As the result of a tender offer, merger, consolidation, sale of assets, or contested election, or any combination of such transactions, the persons who were members of the Board of the Company immediately before the transaction, cease to constitute at least a majority thereof.

Section 11. General Restrictions

Delivery of Common Shares or other amounts under the Plan shall be subject to the following:

(a) Notwithstanding any other provision of the Plan, the Company shall have no liability to deliver any Common Shares under the Plan or make any other distribution of benefits under the Plan unless such delivery or distribution would comply with all applicable laws (including, without limitation, the requirements of the Securities Act of 1933), and the applicable requirements of any securities exchange or similar entity.

(b) To the extent that the Plan provides for issuance of stock certificates to reflect the issuance of Common Shares, the issuance may be effected on a non-certificated basis, to the extent not prohibited by applicable law or the applicable rules of any stock exchange.

Section 12. Operation and Administration

(a) Administration.

(1) The Plan and all Awards granted pursuant thereto shall be administered by a committee of the Board (the “Committee”), which shall initially be the full Board. The full Board shall remain as the Committee until such time, and times, as the Board, in its sole discretion, designates a lesser number of Board members to serve as the Committee. If the Board designates a Committee of less than the full Board, such Committee shall not include Eligible Directors. If the Committee is made up of less than the full Board, or for any other reason determined by the full Board, the full Board may take any action under the Plan that would otherwise be the responsibility of the Committee.

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(2) The Committee shall have the authority and discretion to interpret and administer the Plan, to establish, amend and rescind any rules and regulations relating to the Plan and to determine the terms and provisions of any Award Agreement made pursuant to the Plan. All questions of interpretation with respect to the Plan, the number of Common Shares or other security, or rights granted and the terms of any Award Agreements, including the timing, pricing, and amounts of Awards, shall be determined by the Committee, and its determination shall be final and conclusive upon all parties in interest. In the event of any conflict between an Award Agreement and this Plan, the terms of this Plan shall govern.

(3) Except to the extent prohibited by applicable law or the applicable rules of a stock exchange, the Committee may delegate to the officers or employees of the Company and its Subsidiaries the authority to execute and deliver such instruments and documents, to do all such acts and things, and to take all such other steps deemed necessary, advisable or convenient for the effective administration of the Plan in accordance with its terms and purpose, except that the Committee may not delegate any discretionary authority with respect to substantive decisions or functions regarding the Plan or Awards thereunder, including, but not limited to, decisions regarding the timing, eligibility, pricing, amount or other material terms of such Awards. Any such delegation may be revoked by the Committee at any time.

(4) To the extent that the Committee determines that the restrictions imposed by the Plan preclude the achievement of the material purposes of the Awards in jurisdictions outside the United States, the Committee will have the authority and discretion to modify those restrictions as the Committee determines to be necessary or appropriate to conform to applicable requirements or practices of jurisdictions outside of the United States.

(b) Unfunded Plan. The Plan shall be unfunded. Neither the Company, a Subsidiary, nor the Board shall be required to segregate any assets that may at any time be represented by Awards made pursuant to the Plan. Neither the Company, a Subsidiary, the Committee, nor the Board shall be deemed to be a trustee of any amounts to be paid under the Plan.

(c) Limits of Liability.

(1) Any liability of the Company or a Subsidiary to any Participant with respect to an Award shall be based solely upon contractual obligations created by the Plan and the Award Agreement.

(2) Neither the Company nor a Subsidiary, nor any member of the Board or of the Committee, nor any other person participating in any determination of any question under the Plan, or in the interpretation, administration or application of the Plan, shall have any liability to any party for any action taken or not taken in good faith under the Plan except as may be expressly provided by statute.

(d) Rights of Participants. Nothing contained in this Plan or in any Award Agreement (or in any other documents related to this Plan or to any Award or Award Agreement) shall confer upon any Participant any right to continue in the service of the Company or a Subsidiary or constitute any contract or limit in any way the right of the Company or a Subsidiary to change such person’s compensation or other benefits or to terminate the service of such person with or without cause.

(e) Duration. The Board adopted the Plan subject to the approval of the shareholders of the Company at the Company’s 2003 Annual General Meeting of its shareholders on May 22, 2003. The date of such shareholder approval shall be the “Effective Date” of the Plan. The Plan shall remain in effect until all Awards under the Plan have been exercised or terminated under the terms of the Plan and applicable Award Agreements, provided, however, that Awards under the Plan may only be granted within ten years from the Effective Date of the Plan.

(f) Form and Time of Elections. Any election required or permitted under the Plan shall be in writing, and shall be deemed to be filed when timely delivered to the Secretary of the Company. Any election to receive a Retainer Award in lieu of cash shall be irrevocable after it is filed with respect to the Plan Year for which it is filed, and such

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election shall remain in effect and be irrevocable with respect to any future Plan Year unless a new election with respect to such Plan Year is filed in accordance with rules established by the Committee, in which case such new election shall be irrevocable with respect to such Plan Year.

(g) Action by Company. Any action required or permitted to be taken by the Company shall be by resolution of the Board, or by action of one or more members of the Board (including a committee of the Board) who are duly authorized to act for the Board or (except to the extent prohibited by the provisions of Rule 16b-3, applicable local law, the applicable rules of any stock exchange, or any other applicable rules) by a duly authorized officer of the Company.

(h) Gender and Number. Where the context admits, words in any gender shall include any other gender, words in the singular shall include the plural and the plural shall include the singular.

Section 13. Amendment and Termination

The Board may at any time amend, suspend or discontinue the Plan, in whole or in part; provided, however, that no amendment by the Board shall increase any limitations set forth in Section 7 nor shall it permit any Options to be awarded at Exercise Prices below Fair Market Value without approval of the shareholders. The Committee may at any time alter or amend any or all Award Agreements under the Plan to the extent permitted by law, but no such alteration or amendment shall impair the rights of any holder of an Award without the holder’s consent. Adjustments pursuant to Section 9 shall not be subject to the foregoing limitations of this Section 13.

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