<PAGE>
                                                                     Exhibit 3.1

 
                           CERTIFICATE OF AMENDMENT

                                     TO THE

                     RESTATED CERTIFICATE OF INCORPORATION

                                       OF

                           EDGE PETROLEUM CORPORATION


     Edge Petroleum Corporation (the "Corporation"), a corporation organized and
existing under and by virtue of the General Corporation Law of the State of
Delaware (the "DGCL"), hereby adopts this Certificate of Amendment (this
"Certificate of Amendment"), which amends its Restated Certificate of
Incorporation, as heretofore amended (the "Certificate of Incorporation"), as
described below, and does hereby further certify that:

     1.  The Board of Directors of the Corporation duly adopted a resolution
proposing and declaring advisable the amendment to the Certificate of
Incorporation as described herein, and the Corporation's stockholders duly
adopted such amendment, all in accordance with the provisions of Sections 242
and 228 of the DGCL.

     2.  The Certificate of Incorporation is hereby amended by deleting Article
Fourth thereof and replacing in lieu thereof a new Article Fourth reading in its
entirety as follows:

     FOURTH:  The aggregate number of shares of capital stock that the
Corporation shall have authority to issue is Thirty Million (30,000,000),
divided into Twenty-five Million (25,000,000) shares of common stock, par value
$0.01 per share ("Common Stock"), and Five Million (5,000,000) shares of
preferred stock, par value $0.01 per share ("Preferred Stock").  Shares of any
class of capital stock of the Corporation may be issued for such consideration
and for such corporate purposes as the Board of Directors of the Corporation
(the "Board of Directors")  may from time to time determine.  Each share of
Common Stock shall be entitled to one vote.

     The Preferred Stock may be divided into and issued from time to time in one
or more series as may be fixed and determined by the Board of Directors.  The
relative rights and preferences of the Preferred Stock of each series shall be
such as shall be stated in any resolution or resolutions adopted by the Board of
Directors setting forth the designation of the series and fixing and determining
the relative rights and preferences thereof, any such resolution or resolutions
being herein called a "Directors' Resolution."  The Board of Directors is hereby
authorized to fix and determine the powers, designations, preferences, and
relative, participating, optional or other rights (including, without
limitation, voting powers, full or limited, preferential rights to receive
dividends or assets upon liquidation, rights of conversion or exchange into
Common Stock, Preferred Stock of any series or other securities, any right of
the Corporation to exchange or convert shares into Common Stock, Preferred Stock
of any series or other securities, or redemption provisions or sinking fund
provisions) as between series and as between the Preferred Stock or any series
thereof and the Common Stock, and the qualifications, limitations or
restrictions thereof, if any, all as shall be stated

                                       1
<PAGE>
 
in a Directors' Resolution, and the shares of Preferred Stock or any series
thereof may have full or limited voting powers, or be without voting powers, all
as shall be stated in a Directors' Resolution.

     No stockholder shall, by reason of the holding of shares of any class or
series of capital stock of the Corporation, have a preemptive or preferential
right to acquire or subscribe for any shares or securities of any class, whether
now or hereafter authorized, which may at any time be issued, sold or offered
for sale by the Corporation, unless specifically provided for in a Directors'
Resolution with respect to a series of Preferred Stock.  Furthermore, Common
Stock is not convertible, redeemable or assessable, or entitled to the benefits
of any sinking fund.

     Cumulative voting of shares of any class or series of capital stock having
voting rights is prohibited unless specifically provided for in a Directors'
Resolution with respect to a series of Preferred Stock.

     IN WITNESS WHEREOF, the Corporation has caused this certificate to be
executed this 31st day of January, 1997.

                                    EDGE PETROLEUM CORPORATION



                                    By: /s/ John E. Calaway
                                       ------------------------- 
                                        John E. Calaway
                                        Chief Executive Officer

                                       2
<PAGE>
 
                     RESTATED CERTIFICATE OF INCORPORATION

                                       OF

                           EDGE PETROLEUM CORPORATION

          Edge Petroleum Corporation (the "Corporation"), a corporation
organized and existing under and by virtue of the General Corporation Law of the
State of Delaware (the "DGCL"), hereby adopts this Restated Certificate of
Incorporation, which accurately restates and integrates the provisions of the
existing Certificate of Incorporation of the Corporation and all amendments
thereto that are in effect on the date hereof (the "Certificate of
Incorporation") and further amends the provisions of the Certificate of
Incorporation as described below, and does hereby further certify that:

          1.   The name of the Corporation is Edge Petroleum Corporation and the
original certificate of incorporation of the Corporation was filed with the
Secretary of State of the State of Delaware on August 13, 1996.

          2.   The Board of Directors of the Corporation duly adopted a
resolution proposing and declaring advisable the amendments to the Certificate
of Incorporation as described herein, and the Corporation's sole stockholder
duly adopted such amendments, all in accordance with the provisions of Sections
228, 242 and 245 of the DGCL.

          3.   The Certificate of Incorporation is hereby restated and further
amended to read in its entirety as follows:


                     RESTATED CERTIFICATE OF INCORPORATION

           FIRST: The name of the Corporation is Edge Petroleum Corporation
(hereinafter the "Corporation").

          SECOND: The address of the registered office of the Corporation in the
State of Delaware is 1209 Orange Street, in the City of Wilmington, County of
New Castle. The name of its registered agent at such address is The Corporation
Trust Company.

          THIRD: The purpose of the Corporation is to engage in any lawful act
or activity for which corporations may be organized under the General
Corporation Law of Delaware or any successor statute (the "DGCL").
 
          FOURTH: The aggregate number of shares of capital stock that the
Corporation shall have authority to issue is Fifty Million (50,000,000), divided
into Forty Million (40,000,000) shares of common stock, par value $0.01 per
share ("Common Stock"), and Ten Million (10,000,000) shares of preferred stock,
par value $0.01 per share ("Preferred Stock"). Shares of any

                                       3
<PAGE>
 
class of capital stock of the Corporation may be issued for such consideration
and for such corporate purposes as the Board of Directors of the Corporation
(the "Board of Directors")  may from time to time determine.  Each share of
Common Stock shall be entitled to one vote.

          The Preferred Stock may be divided into and issued from time to time
in one or more series as may be fixed and determined by the Board of Directors.
The relative rights and preferences of the Preferred Stock of each series shall
be such as shall be stated in any resolution or resolutions adopted by the Board
of Directors setting forth the designation of the series and fixing and
determining the relative rights and preferences thereof, any such resolution or
resolutions being herein called a "Directors' Resolution."  The Board of
Directors is hereby authorized to fix and determine the powers, designations,
preferences, and relative, participating, optional or other rights (including,
without limitation, voting powers, full or limited, preferential rights to
receive dividends or assets upon liquidation, rights of conversion or exchange
into Common Stock, Preferred Stock of any series or other securities, any right
of the Corporation to exchange or convert shares into Common Stock, Preferred
Stock of any series or other securities, or redemption provisions or sinking
fund provisions) as between series and as between the Preferred Stock or any
series thereof and the Common Stock, and the qualifications, limitations or
restrictions thereof, if any, all as shall be stated in a Directors' Resolution,
and the shares of Preferred Stock or any series thereof may have full or limited
voting powers, or be without voting powers, all as shall be stated in a
Directors' Resolution.

          No stockholder shall, by reason of the holding of shares of any class
or series of capital stock of the Corporation, have a preemptive or preferential
right to acquire or subscribe for any shares or securities of any class, whether
now or hereafter authorized, which may at any time be issued, sold or offered
for sale by the Corporation, unless specifically provided for in a Directors'
Resolution with respect to a series of Preferred Stock. Furthermore, Common
Stock is not convertible, redeemable or assessable, or entitled to the benefits
of any sinking fund.

          Cumulative voting of shares of any class or series of capital stock
having voting rights is prohibited unless specifically provided for in a
Directors' Resolution with respect to a series of Preferred Stock.

          FIFTH: (a) Directors. The business and affairs of the Corporation
shall be managed by or under the direction of the Board of Directors. In
addition to the authority and powers conferred upon the Board of Directors by
the DGCL or by the other provisions of this Restated Certificate of
Incorporation, the Board of Directors is hereby authorized and empowered to
exercise all such powers and do all such acts and things as may be exercised or
done by the Corporation, subject to the provisions of the DGCL, this Restated
Certificate of Incorporation and any Bylaws adopted by the stockholders of the
Corporation; provided, however, that no Bylaws hereafter adopted by the
stockholders of the Corporation, or any amendments thereto, shall invalidate any
prior act of the Board of Directors that would have been valid if such Bylaws or
amendment had not been adopted.

          (b) Number, Election and Terms of Directors.  The number of directors
that shall constitute the whole Board of Directors shall be fixed from time to
time by a majority of the directors then in office, but shall not be less than
three nor more than twelve, except in the case of an increase in the number of
directors by reason of any provisions contained in or established 

                                       4
<PAGE>
 
pursuant to Article Fourth. The directors, other than those who may be elected
by the holders of any series of Preferred Stock, shall be divided into three
classes, Class I, Class II and Class III. Each director shall serve for a term
ending on the third annual meeting following the annual meeting at which such
director was elected; provided, however, that Stanley S. Raphael is hereby
appointed to Class I and shall serve for a term expiring at the annual meeting
next following the end of the calendar year 1997, that each of Vincent Andrews,
David B. Benedict and Nils Peterson is hereby appointed to Class II and shall
serve for a term expiring at the annual meeting next following the end of the
calendar year 1998, and that each of John E. Calaway, James D. Calaway and John
Sfondrini is hereby appointed to Class III and shall serve for a term expiring
at the annual meeting next following the end of the calendar year 1999. Each
director shall hold office until the annual meeting at which such director's
term expires and, the foregoing notwithstanding, shall serve until his successor
shall have been duly elected and qualified or until his earlier death,
resignation or removal.

          At each annual election, the directors chosen to succeed those whose
terms then expire shall be of the same class as the directors they succeed,
unless, by reason of any intervening changes in the authorized number of
directors, the Board of Directors shall designate one or more directorships
whose term then expires as directorships of another class in order more nearly
to achieve equality of number of directors among the classes.

          In the event of any change in the authorized number of directors, each
director then continuing to serve as such shall nevertheless continue as a
director of the class of which he is a member until the expiration of his
current term, or his prior death, resignation or removal. The Board of Directors
shall specify the class to which a newly created directorship shall be
allocated.

          Election of directors need not be by written ballot unless the Bylaws
of the Corporation shall so provide.

          (c) Removal of Directors.  No director of the Corporation shall be
removed from office as a director by vote or other action of the stockholders or
otherwise except for cause, and then only by the affirmative vote of the holders
of at least a majority of the voting power of all outstanding shares of capital
stock of the Corporation generally entitled to vote in the election of
directors, voting together as a single class.  Except as may otherwise be
provided by law, cause for removal of a director shall be deemed to exist only
if:  (i) the director whose removal is proposed has been convicted, or when a
director is granted immunity to testify when another has been convicted, of a
felony by a court of competent jurisdiction and such conviction is no longer
subject to direct appeal; (ii) such director has been found by the affirmative
vote of a majority of the entire Board of Directors at any regular or special
meeting of the Board of Directors called for that purpose or by a court of
competent jurisdiction to have been grossly negligent or guilty of misconduct in
the performance of his duties to the Corporation in a matter of substantial
importance to the Corporation; or (iii) such director has been adjudicated by a
court of competent jurisdiction to be mentally incompetent, which mental
incompetency directly affects his ability as a director of the Corporation.

          (d) Vacancies.  Except as provided in Article Fourth hereof, newly
created directorships resulting from any increase in the number of directors and
any vacancies on the Board of Directors resulting from death, resignation,
removal or other cause shall be filled by the affirmative vote of a majority of
the remaining directors then in office, even though less than a 

                                       5
<PAGE>
 
quorum of the Board of Directors. Any director elected in accordance with the
preceding sentence shall hold office for the remainder of the full term of the
class of directors in which the new directorship was created or the vacancy
occurred and until such director's successor shall have been elected and
qualified or until his earlier death, resignation or removal. No decrease in the
number of directors constituting the Board of Directors shall shorten the term
of any incumbent director.

          SIXTH: From and after the first date of the closing of the initial
public offering of the Common Stock to the public for cash that has been
registered on a registration statement that has been filed with and declared
effective by the Securities and Exchange Commission, any action required or
permitted to be taken by the stockholders of the Corporation must be effected at
an annual or special meeting of stockholders of the Corporation and may not be
effected by any consent in writing by such stockholders. Except as otherwise
required by law, or as may be prescribed in a Directors' Resolution, special
meetings of stockholders of the Corporation may be called only by the Chairman
of the Board of Directors, or by the Chief Executive Officer of the Corporation
or by the President of the Corporation or by the Board of Directors pursuant to
a resolution approved by the affirmative vote of a majority of the entire Board
of Directors.

          SEVENTH: No director of the Corporation shall be personally liable to
the Corporation or any of its stockholders for monetary damages for breach of
fiduciary duty as a director; provided, however, that the foregoing provisions
shall not eliminate or limit the liability of a director (i) for any breach of
such director's duty of loyalty to the Corporation or its stockholders, (ii) for
acts or omissions not in good faith or which involve intentional misconduct or a
knowing violation of law, (iii) under Section 174 of the DGCL, as the same
exists or as such provision may hereafter be amended, supplemented or replaced,
or (iv) for any transactions from which such director derived an improper
personal benefit. If the DGCL is amended after the filing of this Certificate of
Incorporation to authorize corporate action further eliminating or limiting the
personal liability of directors, then the liability of a director of the
Corporation, in addition to the limitation on personal liability provided
herein, shall be limited to the fullest extent permitted by such law, as so
amended. Any repeal or modification of this Article Seventh by the stockholders
of the Corporation shall be prospective only, and shall not adversely affect any
limitation on the personal liability of a director of the Corporation existing
at the time of such repeal or modification.

          EIGHTH: In furtherance of, and not in limitation of, the powers
conferred by statute, the Board of Directors is expressly authorized to adopt,
amend or repeal the Bylaws of the Corporation, or adopt new Bylaws, without any
action on the part of the stockholders, except as may be otherwise provided by
applicable law or the Bylaws of the Corporation.

          NINTH: Whenever a compromise or arrangement is proposed between the
Corporation and its creditors or any class of them and/or between the
Corporation and its stockholders or any class of them, any court of equitable
jurisdiction within the State of Delaware may, on the application in a summary
way of the Corporation or of any creditor or stockholder thereof, or on the
application of any receiver or receivers appointed for the Corporation under
Section 291 of Title 8 of the Delaware Code, or on the application of trustees
in dissolution or of any receiver or receivers appointed for the Corporation
under Section 279 of Title 8 of the Delaware Code, order a meeting of the
creditors or class of creditors, and/or of the stockholders or class of
stockholders of the Corporation, as the case may be, to be summoned in such
manner as the said 

                                       6
<PAGE>
 
court directs. If the majority in number representing three-fourths in value of
the creditors or class of creditors, and/or of the stockholders or class of
stockholders, of the Corporation, as the case may be, agree to any compromise or
arrangement and to any reorganization of the Corporation as a consequence of
such compromise or arrangement, the said compromise or arrangement and the said
reorganization shall, if sanctioned by the court to which the said application
has been made, be binding on all the creditors or class of creditors, and/or on
all the stockholders or class of stockholders, of the Corporation, as the case
may be, and also on the Corporation.

          IN WITNESS WHEREOF, the Corporation has caused this certificate to be
executed this 27th day of January, 1997.

                                    EDGE PETROLEUM CORPORATION


                                    By:/s/ James D. Calaway
                                       -----------------------------
                                       James D. Calaway
                                       President

                                       7