Exhibit 10.4


                               SEVERANCE AGREEMENT
                               -------------------


Agreement  between  Edge  Petroleum  Corporation,  a Delaware  Corporation  (the
"Company"), and ___________________.


                                   WITNESSETH:
                                   -----------

WHEREAS,  the Company  desires to retain  certain key  employee  personnel  and,
accordingly,  the Board of Directors  of the Company (the  "Board") has approved
the Company  entering  into a severance  agreement  with  Executive  in order to
encourage his continued service to the Company; and

WHEREAS,  Executive  is prepared to commit such  services in return for specific
arrangements with respect to severance compensation and other benefits;

NOW THEREFORE, in consideration of the foregoing and for other good and valuable
consideration, the Company and Executive agree as follows:

1.       Definitions
         -----------

(a)           "Change in Duties"  shall  mean the  occurrence,  within two years
              after the date upon which a Change of Control  occurs,  of any one
              or more of the following:

              (i)     A  significant  reduction in the duties of Executive  from
                      those  applicable to him immediately  prior to the date on
                      which a Change of Control occurs,

              (ii)    A  reduction  in  Executive's   annual  salary  or  target
                      opportunity   under  any  applicable  bonus  or  incentive
                      compensation  plan from that  provided to him  immediately
                      prior to the date on which a Change of Control occurs;

              (iii)   Receipt of employee benefits  (including,  but not limited
                      to medical, dental, life insurance,  accidental death, and
                      dismemberment,   and  long-term   disability   plans)  and
                      perquisites by Executive that are materially  inconsistent
                      with the employee benefits and perquisites provided by the
                      Company to executives with comparable duties;

               (iv)   A change in the location of Executive's principal place of
                      employment  by the  Company by more than 50 miles from the
                      location  where he was  principally  employed  immediately
                      prior to the date on which a Change of Control occurs, or

                (v)   A  change  encompassed  by  paragraph  2.3  (i)(c)  of the
                      Employment Agreement dated November 16, 1998, between
                      Executive and the Company.

        (b)                "Change of Control" means the occurrence of either of
                           the following events:


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<PAGE>

               (i)    The Company (A) shall not be the  surviving  entity in any
                      merger, consolidation or other reorganization (or survives
                      only as a subsidiary  of an entity other than a previously
                      wholly-owned  subsidiary  of the  Company) or (B) is to be
                      dissolved  and  liquidated,  and  as a  result  of  or  in
                      connection  with such  transaction,  the  persons who were
                      directors  of the Company  before such  transaction  shall
                      cease to constitute a majority of the Board;

               (ii)   Any person or entity,  including a "group" as contemplated
                      by Section  13(d)(3)  of the  Securities  Exchange  Act of
                      1934, as amended,  acquires or gains  ownership or control
                      (including,  without limitation,  power to vote) of 20% or
                      more of the  outstanding  shares of the  Company's  voting
                      stock (based upon voting power),  and as a result of or in
                      connection  with such  transaction,  the  persons who were
                      directors  of the Company  before such  transaction  shall
                      cease to constitute a majority of the Board; or

               (iii)  The Company sells all or  substantially  all of the assets
                      of the Company to any other person or entity (other than a
                      wholly-owned  subsidiary  of the Company) in a transaction
                      that requires  shareholder  approval pursuant to the Texas
                      Business Corporation Act.

        (c)                "Code" shall mean the Internal  Revenue Code of 1986,
                           as amended.

        (d)                "Compensation" shall mean the greater of:

               (i)    Executive's  annual  salary  plus his  Targeted  Incentive
                      Award  immediately  prior to the date on which a Change of
                      Control occurs, or

               (ii) Executive's  annual salary plus his Targeted Incentive Award
at the time of his Involuntary Termination.

        (e)    "Incentive  Award"  shall  mean the  amount of any  award  issued
               pursuant to the Edge Petroleum  Corporation  Incentive Award Plan
               or any plan or program successor thereto.

        (f)    "Involuntary   Termination"   shall  mean  any   termination   of
               Executive's employment with the Company which:

               (i)    does not result from a  resignation  by  Executive  (other
                      than  a  resignation  pursuant  to  Clause  (ii)  of  this
                      paragraph  (f)) or a  resignation  at the  request  of the
                      Company; or

               (ii)   results from a  resignation  by Executive on or before the
                      date  which is  sixty  days  after  the  date  upon  which
                      Executive receives notice of a Change in Duties; provided,
                      however,  the term  "Involuntary  Termination"  shall  not
                      include a Termination  for Cause or any  termination  as a
                      result of death,  disability under circumstances entitling
                      him to benefits under the Company's  long-term  disability
                      plan, or Retirement.

         (g)      "Retirement" shall mean Executive's  voluntary  resignation on
                  or after  December 31, 2006 (other than a  resignation  within
                  sixty  days  after  the date  Executive  receives  notice of a
                  change  in  Duties  or a  resignation  at the  request  of the
                  Company).


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          (h)     "Severance Amount" shall mean an amount equal to _______ times
                  Executive's Compensation,  reduced by the present value of any
                  salary  continuation  payments  payable to Executive under the
                  Employment  Agreement  between the  Company and the  Executive
                  effective  as of November 16, 1998 or any  successor  thereto.
                  Such  present  value  shall be  determined  using  the rate of
                  interest  referred to in Paragraph 4 hereof as of the last day
                  of Executive's employment with the Company.

           (i)    "Targeted  Incentive Award" shall mean  Executive's  Incentive
                  Target,  if any, as set forth under the  Incentive  Award Plan
                  effective  for the year with  respect  to which  such award is
                  being  determined,  if any, or for the last  preceding year in
                  which an Incentive Award was in effect,  expressed as a dollar
                  amount based on such Executive's annual salary for such year.

           (j)    "Termination  for Cause" shall mean termination of Executive's
                  employment by the Company (or its  subsidiaries)  by reason of
                  Executive's  gross   negligence,   gross  neglect  or  willful
                  misconduct  in the  performance  of his duties or  Executive's
                  final  conviction  of a felony or of a  misdemeanor  involving
                  moral turpitude, excluding misdemeanor convictions relating to
                  the operation of a motor vehicle.

           (k)    "Welfare Benefit  Coverages"  shall mean the medical,  dental,
                  life,  insurance,   accidental  death  and  dismemberment  and
                  long-term  disability coverages provided by the Company to its
                  active employees.

2.         Services.  Executive  agrees  that he  will  render  services  to the
           Company  (as well as any  subsidiary  thereof or  successor  thereto)
           during the period of his employment to the best of his ability and in
           a prudent and businesslike manner.

3.         Severance Benefits.  If Executive's  employment by the Company or any
           subsidiary  thereof  or  successor  thereto  shall be  subject  to an
           Involuntary  Termination which occurs within two years after the date
           upon  which a Change  of  Control  occurs,  then  Executive  shall be
           entitled to receive, as additional compensation for services rendered
           to the Company (including its subsidiaries),  the following severance
           benefits:

           (a)    A lump sum cash  payment  in an  amount  equal to  Executive's
                  Severance Amount.

           (b)    A lump sum cash  payment in an amount  equal to the  remaining
                  portion  of any award to  Executive  under  any  prior  years'
                  Incentive   Award.   Further,   if   Executive's   Involuntary
                  Termination  occurs  on or after  the  date an award  has been
                  earned under the Incentive  Award Plan,  but prior to the date
                  such award is paid, Executive shall receive an additional lump
                  sum cash  payment in an amount  equal to his Target  Incentive
                  Award.

           (c)      Executive  shall be entitled to continue the Welfare Benefit
                    Coverages for himself and,  where  applicable,  his eligible
                    dependents  following his Involuntary  Termination for up to
                    thirty-six months, as long as Executive  continues either to
                    pay the premiums paid by active employees of the Company for
                    such coverages or to pay the actual  (nonsubsidized) cost of
                    such  coverages for which the Company does not subsidize for
                    active  employees.  Such benefit  rights shall apply only to
                    those  Welfare  Benefit  Coverages  which the Company has in
                    effect  from  time to time  for  active  employees,  and the
                    applicable  payments  shall  adjust as  premiums  for active
                    employees  of the  Company  or actual  costs,  whichever  is
                    applicable, change.


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<PAGE>


                    Welfare  Benefit  Coverage(s)  shall  immediately  end  upon
                    Executive's obtainment of new employment and eligibility for
                    similar  Welfare Benefit  coverage(s)  (with Executive being
                    obligated  hereunder to promptly report such  eligibility to
                    the  Company).  Nothing  herein shall be deemed to adversely
                    affect in any way the additional rights, after consideration
                    of this  extension  period,  of  Executive  and his eligible
                    dependents to health care continuation  coverage as required
                    pursuant to Part 6 of Title I of the  Employment  Retirement
                    Income Security Act of 1974, as amended.

           (d)    Executive shall be entitled to receive out-placement  services
                  in connection  with  obtaining new  employment up to a maximum
                  cost of $6,000, if Executive is seeking new employment.

          (e)     The severance  benefits  payable under this agreement shall be
                  paid to the  Executive  on or  before  the fifth day after the
                  last  day of  Executive's  employment  with the  Company.  Any
                  severance  benefits  paid pursuant to this  paragraph  will be
                  deemed to be a severance  payment and not compensation for the
                  purposes of determining benefits under the Company's qualified
                  plans and shall be subject to any required tax withholding.

4.      Interest  on Late  Benefit  Payments.  If any  payment  provided  for in
        Paragraph  3(a) or 3(b) hereof is not made when due,  the Company  shall
        pay to Executive  interest on the amount payable from the date that such
        payment should have been made under such paragraph until such payment is
        made,  which  interest  shall  be  calculated  at a  rate  equal  to two
        percentage  points over the prime or base rate of interest  announced by
        Chase Bank of Texas, N.A. for successor thereto) at its principal office
        in Houston, Texas and shall change when and as such change in such prime
        base rate shall be announced by such bank.

5.      Certain Additional Payments by the Company.  Notwithstanding anything to
        the  contrary  in this  Agreement,  in the  event  that any  payment  or
        distribution by the Company to or for the benefit of Executive,  whether
        paid or  distributed  or  distributable  pursuant  to the  terms of this
        Agreement or otherwise (a "Payment"), would be subject to the excise tax
        imposed by Section 4999 of the Code or any  interest or  penalties  with
        respect to such  excise tax (such  excise  tax,  together  with any such
        interest or penalties,  are hereinafter  collectively referred to as the
        "Excise Tax"), the Company shall pay to Executive an additional  payment
        (a "Gross-up Payment") in an amount such that after payment by Executive
        of all taxes (including an interest or penalties imposed with respect to
        such taxes),  including any Excise Tax imposed on any Gross-up  Payment,
        Executive  retains an amount of the Gross-up Payment equal to the Excise
        Tax imposed upon the payment.  The Company and  Executive  shall make an
        initial  determination  as to whether a Gross-up Payment is required and
        the amount of any such  Gross-up  Payment.  Executive  shall  notify the
        Company in writing of any claim by the Internal  Revenue  Service which,
        if successful,  would require the Company to make a Gross-up Payment (or
        a Gross-up  Payment in excess of that, if any,  initially  determined by
        the Company and Executive) within ten days of the receipt of such claim.
        The Company shall notify Executive in writing at least ten days prior to
        the due date of any response  required  with respect to such claim if it
        plans to  contest  the claim.  If the  Company  decides to contest  such
        claim,  Executive shall cooperate fully with the Company in such action;
        provided, however, the Company shall bear and pay directly or indirectly
        all cost and expenses  (including  additional  interest  and  penalties)
        incurred in  connection  with such action and shall  indemnify  and hold
        Executive harmless,  on an after-tax basis, for any Excise Tax or income
        tax, including interest and penalties with respect thereto, imposed as a
        result of the Company's

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<PAGE>

        action. If, as a result of the Company's action with respect to a claim,
        Executive  receives  a refund of any  amount  paid by the  Company  with
        respect to such claim,  Executive  shall promptly pay such refund to the
        Company. If the Company fails to timely notify Executive whether it will
        contest such claim or the Company  determines not to contest such claim,
        then the Company shall  immediately pay to Executive the portion of such
        claim, if any, which it has not previously paid to Executive.

6.                General.

        (a)     Term. The effective  date of this Agreement is  _______________.
                The initial term of this Agreement shall be the period beginning
                on said effective date and ending on the two-year anniversary of
                said effective  date.  Within sixty days after the expiration of
                this  Agreement  and within  sixty  days  after each  successive
                two-year  period of time  thereafter  that this  Agreement is in
                effect,  the  Company  shall  have  the  right  to  review  this
                Agreement, and in its sole discretion either continue and extend
                this Agreement, terminate this Agreement, and/or offer Executive
                a different  agreement.  The Board  (excluding any member of the
                Board who is covered by this Agreement or by a similar agreement
                with the Company) will vote on whether to so extend,  terminate,
                and/or  offer  Executive a different  agreement  and will notify
                Executive of such action before the end of said  sixty-day  time
                period  mentioned  above.  This Agreement shall remain in effect
                until so terminated  and/or modified by the Company.  Failure of
                the Board to take any action within said  sixty-day  time period
                shall be  considered  as an extension of this  Agreement  for an
                additional two-year period of time.  Notwithstanding anything to
                the contrary contained in this "sunset  provision," it is agreed
                that if a Change of Control  occurs  while this  Agreement is in
                effect,  then this Agreement shall not be subject to termination
                or modification under this "sunset  provision," and shall remain
                in force for a period of two years after such Change of Control,
                and if within said two years the contingency factors occur which
                would entitle Executive to the benefits as provided herein, this
                Agreement  shall remain in effect in accordance  with its terms.
                If,  within  such two  years  after a  Change  of  Control,  the
                contingency   factors  that  would  entitle  Executive  to  said
                benefits  do  not  occur,   thereupon   this  two-year   "sunset
                provision"  shall again be applicable  with the  sixty-day  time
                period  for  Board  action  shall  thereafter  commence  at  the
                expiration of said two years after such Change of Control and on
                each two-year anniversary date thereafter.

        (b)     Indemnification. If Executive shall obtain any money judgment or
                otherwise  prevail  with  respect to any  litigation  brought by
                Executive or the Company to enforce or interpret  any  provision
                contained herein,  the Company,  to the fullest extent permitted
                by  applicable  law,  hereby   indemnifies   Executive  for  his
                reasonable  attorneys' fees and  disbursements  incurred in such
                litigation  and  hereby  agrees (i) to pay in full all such fees
                and  disbursements  and (ii) to pay prejudgment  interest on any
                money judgment obtained by Executive from the earliest date that
                payment to him should have been made under this Agreement  until
                such judgment shall have been paid in full, which interest shall
                be calculated at a rate equal to two percentage  points over the
                prime or base rate of interest announced by Chase Bank of Texas,
                N.A.  (or any  successor  thereto)  at its  principal  office in
                Houston,  Texas, and shall change when and as any such change in
                such prime or base rate shall be announced by such bank.

        (c)     Payment Obligations Absolute. The Company's obligation to pay or
                cause one of its  subsidiaries to pay) Executive the amounts and
                to make the  arrangement  provided  herein shall be absolute and
                unconditional and shall not be affected by any


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<PAGE>

                circumstances,   including,  without  limitation,  any  set-off,
                counterclaim,  recoupment,  defense  or other  right  which  the
                Company  (including  its  subsidiaries)  may have against him or
                anyone else. All amounts  payable by the Company  (including its
                subsidiaries  hereunder) shall be paid without notice or demand.
                Executive  shall not be  obligated to seek other  employment  in
                mitigation of the amounts payable or arrangements made under any
                provision  of  this  Agreement,   and,  except  as  provided  in
                Paragraph  3  (c)  hereof,  the  obtaining  of  any  such  other
                employment  shall  in no  event  effect  any  reduction  of  the
                Company's obligations to make (or cause to be made) the payments
                and arrangements required to be made under this Agreement.

        (d)    Successors. This Agreement shall be binding upon and inure to the
               benefit of the  Company  and any  successor  of the  Company,  by
               merger,  combination,  asset sale or  otherwise.  This  Agreement
               shall also be binding  upon and inure to the benefit of Executive
               and his estate.  If Executive  shall die prior to full payment of
               amounts due pursuant to this  Agreement,  such  amounts  shall be
               payable pursuant to the terms of this Agreement to his estate.

        (e)    Severability. Any provision in this Agreement which is prohibited
               or  unenforceable in any jurisdiction by reason of applicable law
               shall, as to such jurisdiction, be ineffective only to the extent
               of such prohibition or unenforceability  without  invalidating or
               affecting  the  remaining   provisions   hereof,   and  any  such
               prohibition or  unenforceability  in any  jurisdiction  shall not
               invalidate or render  unenforceable  such  provision in any other
               jurisdiction.

(f)            Non-Alienation.  Executive  shall not have any  right to  pledge,
               hypothecate,  anticipate  or assign this  Agreement or the rights
               hereunder,   except   by  will  or  the  laws  of   descent   and
               distribution.

        (g)    Notices. Any notices or other communications provided for in this
               Agreement  shall  be  sufficient  if in  writing.  In the case of
               Executive,  such notices or  communications  shall be effectively
               delivered if hand  delivered to Executive at his principal  place
               of  employment  or if sent by  registered  or  certified  mail to
               Executive at the last  address he has filed with the Company.  In
               the case of the Company,  such notices or communications shall be
               effectively  delivered if sent by registered or certified mail to
               the Company at its principal executive offices.

        (h)    Controlling  Law.  This  Agreement  shall  be  governed  by,  and
               construed  in  accordance  with,  the laws of the State of Texas.
               Further,  Executive  agrees that any legal  proceeding to enforce
               the  provisions  of this  Agreement  shall be brought in Houston,
               Harris  County,  Texas,  and hereby waives his right to any pleas
               regarding subject matter or personal jurisdiction and venue.

        (i)    Release.  As a  condition  to the  receipt of any  benefit  under
               paragraph 3 hereof,  Executive shall first execute a release,  in
               the form established by the Company,  releasing the Company,  its
               shareholders, partners, officers, directors, employees and agents
               from any and all  claims and from any and all causes of action of
               any  kind  or  character   (except   claims  arising  under  this
               Agreement),  including but not limited to all claims or causes of
               action arising out of Executive's employment with the Company or,
               with the  exception  of  rights  provided  in any  other  written
               agreement  between the Company and Executive,  the termination of
               such employment.


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        (j)    Full  Settlement.  If  Executive  is entitled to and receives the
               benefits  provided  hereunder,  performance of the obligations of
               the Company  hereunder  will  constitute  full  settlement of all
               claims that executive might otherwise  assert against the Company
               on account of this termination of employment,  except such claims
               as may be asserted  pursuant to any other  agreement  between the
               Company and Executive.

        (k)    Unfunded  Obligation.  The  obligation  to pay amounts under this
               Agreement is an unfunded obligation of the Company (including its
               subsidiaries),  and no such obligation shall create a trust or be
               deemed to be secured by any pledge or encumbrance on any property
               of the Company (including its subsidiaries).

        (l)    Not a Contract of Employment.  This Agreement shall not be deemed
               to constitute a contract of  employment,  nor shall any provision
               hereof affect (i) the right of the Company (or its  subsidiaries)
               to discharge Executive at will, subject to the terms of any other
               agreement   between  the  Company  (or  its   subsidiaries)   and
               Executive,  or  (ii)  the  terms  and  conditions  of  any  other
               agreement  between the Company and  Executive  except as provided
               herein.

        (m)    Number and Gender. Wherever appropriate herein, words used in the
               singular  shall  include the plural and the plural shall  include
               the singular.  The masculine  gender where appearing herein shall
               be deemed to include the feminine gender.

        (n)    Counterparts.  This  Agreement  may be  executed  in one or  more
               counterparts,  each of which  shall be deemed to be an  original,
               but all of  which  together  will  constitute  one  and the  same
               Agreement.

        (o)    Headings. The headings in this Agreement are for convenience only
               and shall be disregarded in construing this Agreement.

IN WITNESS  WHEREOF,  THE PARTIES  HERETO HAVE  EXECUTED  THIS  AGREEMENT ON THE
_________ DAY OF ___________________, 19_____.


                                                "Executive"

                                                --------------------------------

                                                John W. Elias

                                                 "Company"
                                                 Edge Petroleum Corporation

                                           By:  ______________________________

                                         Name:  Vincent S. Andrews
                                        Title:  Chairman, Compensation Committee
                                                of Board of Directors


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<PAGE>


Agreements  identical  to the  forgoing  were  entered  into by and between Edge
Petroleum  Corporation  and Officers of the Company and  differences  are listed
within the following schedule:


                                    Schedule
                                    --------

                                    Severance
Name                           Amount (per Sec. 1.h)
----                           ---------------------
John W. Elias                          2.99
Michael G. Long                        2.00
Brian C. Baumler                       1.25

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