<PAGE>   1
                                                                    EXHIBIT 3.1



                     RESTATED CERTIFICATE OF INCORPORATION

                                       OF

                         THE RESERVE PETROLEUM COMPANY


     THE RESERVE PETROLEUM COMPANY, a corporation organized and existing under
the laws of the State of Delaware, hereby certifies as follows:

     1. The name of the corporation is THE RESERVE PETROLEUM COMPANY and the
name under which the corporation was originally incorporated is Farmers Royalty
Holding Co.

     The date of filing its original Certificate of Incorporation with the
Secretary of State was July 18, 1931.

     2. This Restated Certificate of Incorporation only restates and integrates
and does not further amend the provisions of the Certificate of Incorporation
of this corporation as heretofore amended or supplemented and there is no
discrepancy between those provisions and the provisions of this Restated
Certificate of Incorporation.

     3. The text of the Certificate of Incorporation as amended or supplemented
heretofore is hereby restated without further amendments or changes to read as
follows:

     FIRST: The name of the corporation is THE RESERVE PETROLEUM COMPANY.

     SECOND: The registered office of the corporation is to be located in the
     City of Wilmington, in the County of New Castle, in the State of Delaware.
     The name of its registered agent is The Corporation Trust Company, whose
     address is 1209 Orange Street, City of Wilmington, County of New Castle,
     State of Delaware 19801.

     THIRD: The nature of the business of the corporation and the objects or
     purposes proposed to be transacted, promoted or carried on by it, are as
     follows, to wit:

          (1) To acquire, bring together, hold, dispose of and deal in royalty
     and other interests in minerals, and to manage, control and exploit said
     mineral interests, and to collect the revenue arising therefrom;

          (2) To purchase or otherwise acquire, to hold, own, mortgage,
     exchange, pledge, sell, convey, lease, assign, transfer or 




                                     -1-
<PAGE>   2

     otherwise deal or trade in and dispose of goods, wares and merchandise,
     royalties, chattels, patents, trademarks, bonds, mortgages, debentures,
     securities, evidences of indebtedness, stock, shares or rights in
     corporations; and real and personal property, and every estate, interest,
     or rights therein, of any nature or description, and in such franchises,
     goodwill, grants, concessions, as a business corporation may lawfully
     acquire; to receive, collect and dispose of the dividends and interest and
     income on any of said bonds, mortgages, debentures, securities and
     evidences of indebtedness, stock or shares and property held by it and to
     exercise any and all rights, powers and privileges of ownership of any and
     all such stock, shares and properties;

          (3) To the same extent as natural persons might or could do, to
     purchase or otherwise acquire, and to hold, own, maintain, work, develop,
     sell, lease, exchange, hire, convey, mortgage or otherwise dispose of and
     deal in, lands, leaseholds, and especially oil leases, and any interest,
     estate and rights in real property, and any personal or mixed property,
     and any franchises, rights, licenses or privileges necessary, convenient
     or appropriate for any of the purposes herein expressed;

          (4) To act as the agent, proxy or representative otherwise than as
     fiscal or transfer agent of any corporation, firm, or individual, and as
     such to promote, develop and extend the business of such corporation;

          (5) To loan money on bonds secured by mortgage on real property or
     otherwise; to construct, erect, build, improve, and maintain houses and
     buildings of any and every description on any lands of the corporation or
     upon other lands, and to carry on the general business of real estate
     agent and broker;

          (6) To subscribe for, to purchase, invest in, acquire, hold and own;
     and to sell, assign, transfer, pledge, mortgage, exchange, distribute or
     otherwise dispose of the whole or any part of the shares of the capital
     stock, bonds, mortgages, debentures, notes, coupons and other securities,
     obligations, contracts and evidences of indebtedness of any corporation,
     domestic or foreign and to issue in exchange therefor its shares of stock,
     bonds or other obligations and to exercise in respect to any such shares
     of stock, bonds, or other securities or evidences of indebtedness, any and
     all rights and privileges of individual holders or owners including the
     right to vote thereon; and to aid in any manner as permitted by law, any
     corporation or association of which any stock, bonds, or other 


                                      -2-
<PAGE>   3

     securities or evidences of indebtedness are held by or for this company,
     and do any other act or thing designed to protect, preserve, improve or
     enhance the value of any such company or of its stock, bonds or other
     securities or evidences of indebtedness, or to promote or facilitate the
     welfare and business of the corporation or of any subsidiary company;

          (7) To borrow money for the purposes of the corporation and to issue
     bonds, notes and other obligations and to secure the same by pledge or
     mortgage of the whole or part of the property of the corporation, either
     real or personal, or to issue bonds, notes, debentures or other
     obligations without any such security, and to sell or pledge such bonds,
     notes or other obligations for its proper corporate purposes;

          (8) To act as agent for the purchase or sale of property, rights and
     interests of any description and to do any such act or thing connected
     with the above powers; to promote corporations or enterprises of any
     character, including industrial, railroad, steamship, real estate and
     mining companies;

          (9) To conduct and transact its business in any and all its branches
     in any state, territory, colony or dependency of the United States, and
     the District of Columbia and in any and all foreign countries, and to have
     proper offices therein; also to purchase, hold or mortgage and convey real
     or personal property therein without limit, subject always to the laws of
     such state, territory, colony, dependency or foreign country;

          (10) The foregoing clauses shall be construed as objects and powers
     in furtherance and not in limitation of the general powers conferred by
     the laws of the State of Delaware, and it is hereby expressly provided
     that the foregoing enumeration of specific powers shall not be held to
     limit or restrict in any manner the powers of this corporation, and that
     this corporation may do all and everything necessary, suitable and proper
     for the accomplishment of any of the purposes or objects hereinbefore
     enumerated, either alone or in association with other corporations, firms,
     or individuals, to the same extent and as fully as individuals might or
     could do as principals, agents, contractors or otherwise;

          (11) Nothing contained in this Certificate, however, shall be
     construed to authorize this corporation to engage in the banking,
     insurance, railroad or transportation business, or to issue bills, notes
     or other evidence of debt for circulation as money, or to carry 


                                      -3-
<PAGE>   4

     on any business or exercise any power in any state or country unless
     permitted under the laws thereof.

          (12) The business of the company will not be in conflict with, nor
     such as is prohibited by, Title 12, U.S. Code, Sections 584 to 588 and
     Chapter 377, Sections 1 to 15, 44 Statutes at Large, 628-629.

     FOURTH: The total number of shares of stock which the corporation is
     authorized to issue is four hundred thousand (400,000) and the par value
     of each such shares is Fifty Cents ($.50).

     FIFTH: The minimum amount of capital with which the corporation will
     commence business is One Thousand Dollars ($1,000).

     SIXTH: The corporation is to have perpetual existence.

     SEVENTH: The private property of the stockholders shall not be subject to
     the payment of corporate debts to any extent whatever.

     EIGHTH: The following provisions are inserted for the management of the
     business and for the conduct of the affairs of this corporation, and for
     further definition, limitation and regulation of the powers of this
     corporation and of its directors and stockholders:

          (1) The number of directors of the corporation shall be such as from
     time to time shall be fixed by, or in the manner provided in the bylaws,
     but shall not be less than three. In case of any increase in the number of
     directors, the additional directors may be elected by the directors or by
     the stockholders at an annual or special meeting as shall be provided in
     the bylaws.

          (2) By a resolution or resolutions passed by a majority of the whole
     board, the board of directors may designate one or more committees, each
     committee to consist of two or more directors of the corporation, which,
     to the extent provided in said resolution or resolutions or in the bylaws
     of the corporation, shall have and may exercise the powers of the board of
     directors in the management of the business and affairs of the
     corporation, and shall have power to authorize the seal of the corporation
     to be affixed to all papers which may require it. Such committee or
     committees shall have such name or names as may be stated in the


                                      -4-
<PAGE>   5

     bylaws of the corporation, or as may be determined from time to time by
     resolution adopted by the board of directors.

          (3) The board of directors shall have power:

               (a) Without the assent or vote of the stockholders, to make,
          alter, amend, change, add to, or repeal the bylaws of this
          corporation; to fix and vary the amount to be reserved as working
          capital; to authorize and cause to be executed mortgages and liens
          upon all the property of the corporation, or any part thereof; to
          determine the use and disposition of any surplus or net profits over
          and above the capital stock paid in, and to fix the times for the
          declaration and payment of dividends.

               (b) With the consent in writing of the holders of a majority of
          the voting stock issued and outstanding, or upon the affirmative vote
          of the holders of a majority of the stock issued and outstanding
          having voting power, to sell, lease or exchange all of its property
          and assets, including its goodwill and its corporate franchises, upon
          such terms and conditions and for such consideration as the board of
          directors shall deem expedient and for the best interests of the
          corporation.

               (c) To determine from time to time whether, and to what extent,
          and at what times and places, and under what conditions and
          regulations, the accounts and books of the corporation (other than
          the stock ledger) or any of them, shall be open to the inspection of
          the stockholders; and no stockholder shall have any right to inspect
          any account or book or document of the corporation unless expressly
          so authorized by statute or by a resolution of the stockholders or
          the directors.

          (4) The directors in their discretion may submit any contract or act
     for approval or ratification at any annual meeting of the stockholders or
     at any meeting of the stockholders called for the purpose of considering
     any such act or contract, and any contract or act that shall be approved
     or be ratified by the vote of the holders of a majority of the stock of
     the corporation which is represented in person or by proxy at such meeting
     and entitled to vote thereat (provided that a lawful quorum of
     stockholders be there represented in person or by proxy) shall be as valid
     and as binding upon the corporation and upon all the stockholders, as



                                      -5-
<PAGE>   6

     though it had been approved or ratified by every stockholder of the
     corporation, whether or not the contract would otherwise be open to legal
     attack because of directors' interest, or for any other reason.

          (5) In addition to the powers and authorities hereinbefore or by
     statute expressly conferred upon them, the directors are hereby empowered
     to exercise all such powers and do all such acts and things as may be
     exercised or done by the corporation; subject, nevertheless, to the
     provisions of the statutes of Delaware, of this Certificate, and to any
     bylaws from time to time made by the stockholders; provided, however, that
     no bylaw so made shall invalidate any prior act of the directors which
     would have been valid if such bylaw had not been made.

     NINTH: The corporation reserves the right to amend, alter, change or
     repeal any provision contained in this Certificate of Incorporation in the
     manner now or hereafter prescribed by law, and all rights and powers
     conferred herein on stockholders, directors and officers are subject to
     this reserved power.

     TENTH:

          (1) Elimination of Certain Liability of Directors. No director shall
     be personally liable to the corporation or any stockholder for monetary
     damages for breach of fiduciary duty by such director as a director,
     except for any matter in respect of which such director shall be liable
     under Section 174 of the Delaware General Corporation Law or any amendment
     thereto or successor provision thereof or shall be liable by reason that,
     in addition to any and all other requirements for such liability, he (i)
     shall have breached his duty of loyalty to the corporation or its
     stockholders, (ii) in acting or in failing to act, shall not have acted in
     good faith or shall have acted in a manner involving intentional
     misconduct or a knowing violation of law, or (iii) shall have derived an
     improper personal benefit from the transaction in respect of which such
     breach of fiduciary duty occurred. Neither the amendment nor repeal of
     section (1) of this Article Tenth shall eliminate or reduce the effect of
     section (1) of this Article Tenth in respect of any matter occurring, or
     any cause of action, suit or claim that, but for section (1) of this
     Article Tenth would accrue or arise, prior to such amendment or repeal. If
     the Delaware General Corporation Law is amended after approval by the
     stockholders of this Article Tenth to authorize corporate action further
     eliminating or limiting the personal liability of directors, then the
     liability of a 


                                      -6-
<PAGE>   7

     director of the corporation shall be eliminated or limited to the fullest
     extent permitted by the Delaware General Corporation Law, as so amended
     from time to time.

          (2) Indemnification and Insurance.

               (a) Right to Indemnification. Each person who was or is made a
          party or is threatened to be made a party to or is involved in any
          action, suit or proceeding, whether civil, criminal, administrative
          or investigative (hereinafter, a "proceeding"), by reason of the fact
          that he or she, or a person of whom he or she is the legal
          representative, is or was a director or officer of the corporation or
          is or was serving at the request of the corporation as a director or
          officer of another corporation or of a partnership, joint venture,
          trust or other enterprise, including service with respect to employee
          benefit plans maintained or sponsored by the corporation
          (hereinafter, "Corporate Agent"), whether the basis of such
          proceeding is alleged action in an official capacity as a director or
          officer of the corporation or Corporate Agent or in any other
          capacity while serving as a director, officer, or Corporate Agent,
          shall be indemnified and held harmless by the corporation to the
          fullest extent authorized by the Delaware General Corporation Law, as
          the same exists or may hereafter be amended (but, in the case of any
          such amendment, only to the extent that such amendment permits the
          corporation to provide broader indemnification rights than said Law
          permitted the corporation to provide prior to such amendment),
          against all expense, liability and loss (including attorneys' fees,
          judgments, fines, excise taxes pursuant to the Employee Retirement
          Income Security Act of 1974 or penalties and amounts paid or to be
          paid in settlement) reasonably incurred or suffered by such person in
          connection therewith and such indemnification shall continue as to a
          person who has ceased to be a director, officer, or Corporate Agent
          and shall inure to the benefit of his or her heirs, executors and
          administrators; provided, however, that, except as provided in
          paragraph (b) hereof, the corporation shall indemnify any such person
          seeking indemnification in connection with a proceeding (or part
          thereof) initiated by such person only if such proceeding (or part
          thereof) was authorized by the board of directors of the corporation.
          The right to indemnification conferred in this section shall be a
          contractual right and shall include the 


                                      -7-
<PAGE>   8

          right to be paid by the corporation the expenses incurred in
          defending any such proceeding in advance of its final disposition;
          provided, however, that, if the Delaware General Corporation Law
          requires, the payment of such expenses incurred by a director or
          officer in advance of the final disposition of a proceeding shall be
          made only upon delivery to the corporation of an undertaking, by or
          on behalf of such director or officer, to repay all amounts so
          advanced if it shall ultimately be determined that such director or
          officer is not entitled to be indemnified under this section or
          otherwise. The corporation may, by action of its board of directors,
          provide indemnification to employees and other agents of the
          corporation with the same scope and effect as the foregoing
          indemnification of directors, officers, and Corporate Agents.

               (b) Right of Claimant to Bring Suit. If a claim under paragraph
          (a) of this section is not paid in full by the corporation within
          thirty days after a written claim has been received by the
          corporation, the claimant may at any time thereafter bring suit
          against the corporation to recover the unpaid amount of the claim
          and, if successful in whole or in part, the claimant shall be
          entitled to be paid also the expense of prosecuting such claim. It
          shall be a defense to any such action (other than an action brought
          to enforce a claim for expenses incurred in defending any proceeding
          in advance of its final disposition where the required undertaking,
          if any is required, has been tendered to the corporation) that the
          claimant has not met the standard of conduct which makes it
          permissible under the Delaware General Corporation Law for the
          corporation to indemnify the claimant for the amount claimed, but the
          burden of proving such defense shall be on the corporation. Neither
          the failure of the corporation (including its board of directors,
          independent legal counsel, or its stockholders) to have made a
          determination prior to the commencement of such action that
          indemnification of the claimant is proper in the circumstances
          because he or she has met the applicable standard of conduct set
          forth in the Delaware General Corporation Law, nor an actual
          determination by the corporation (including its board of directors,
          independent legal counsel, or its stockholders) that the claimant has
          not met such applicable standard of conduct, shall be a defense to
          the action or create a presumption that the claimant has not met the
          applicable standard of conduct.



                                      -8-
<PAGE>   9

               (c) Non-Exclusivity of Rights. The right to indemnification and
          the payment of expenses incurred in defending a proceeding in advance
          of its final disposition conferred in this section shall not be
          exclusive of any other right which any person may have or hereafter
          acquire under any statute, provision of this Certificate of
          Incorporation, Bylaw, agreement, vote or stockholders or
          disinterested directors, or otherwise.

               (d) Insurance. The corporation may maintain insurance, at its
          expense, to protect itself and any director, officer, employee or
          agent of the corporation or another corporation, partnership, joint
          venture, trust or other enterprise against any such expense,
          liability or loss, whether or not the corporation would have the
          power to indemnify such person against such expense, liability or
          loss under the Delaware General Corporation Law.

     4. This Restated Certificate of Incorporation was duly adopted by the
board of directors in accordance with Section 245 of the General Corporation
Law of the State of Delaware.

     IN WITNESS WHEREOF, said THE RESERVE PETROLEUM COMPANY has caused this
Certificate to be signed by Mason W. McLain, its President, and attested by
Jerry L. Crow, its Secretary, this 1st day of November, 1988.

                                        THE RESERVE PETROLEUM COMPANY

                                        By:  MASON W. MCLAIN
                                             ---------------------------
                                             MASON W. McLAIN, President

ATTEST:

By: JERRY L. CROW
    -------------------------
    JERRY L. CROW, Secretary




                                      -9-