<PAGE>   1
                       SECURITIES AND EXCHANGE COMMISSION
                              Washington, DC 20549

                                   FORM 10-QSB





(Mark One)

      [ X ]      QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15 (d) OF THE
                        SECURITIES EXCHANGE ACT OF 1934

                 For the quarterly period ended March 31, 1998

      [   ]     TRANSITION REPORT PURSUANT TO SECTION 13 OR 15 (d) OF THE
                        SECURITIES EXCHANGE ACT OF 1934

                         Commission file number 0-8157
                         THE RESERVE PETROLEUM COMPANY
       (Exact name of small business issuer as specified in its charter)

           Delaware                                             73-0237060
(State or other jurisdiction of                               (IRS Employer
incorporation or organization)                               Identification No.)

           6801 N. Broadway, Suite 300, Oklahoma City  OK 73116-9092
                    (Address of principal executive offices)

                                 (405) 848-7551
              (Registrant's telephone number, including area code)

Indicate by check mark whether the registrant (1) filed all reports required to
be filed by Section 13 or 15 (d) of the Securities Exchange Act of 1934 during
the preceding 12 months (or for such shorter period that the registrant was
required to file such reports), and (2) has been subject to such filing
requirements for the past 90 days.    Yes [X]    No [ ]

 As of  May 5, 1998, 167,908.73 shares of the Registrant's $.50 par value
common stock were outstanding.

Transitional Small Business Disclosure Format (check one) Yes [ ]  No [X]
<PAGE>   2





                                     PART 1
                             FINANCIAL INFORMATION




                                       2
<PAGE>   3

                         THE RESERVE PETROLEUM COMPANY
                                 BALANCE SHEETS
                                  (Unaudited)
                                     ASSETS
<TABLE>
<CAPTION>
                                                           March 31,        December 31,
                                                              1998             1997
                                                           ----------       ----------
<S>                                                        <C>              <C>       
Current Assets:
    Cash and Cash Equivalents                              $  113,388       $  313,540
    Available for Sale Securities                           3,594,318        3,306,740
    Trading Securities                                        469,851          447,266
    Receivables                                               291,992          278,741
    Refundable Income Taxes                                    25,170           75,424
    Prepayments                                                 3,750            5,625
                                                           ----------       ----------
                                                            4,498,469        4,427,336
                                                           ----------       ----------
 Investments:
   Partnership and Limited
     Liability Companies                                      475,321          490,587
   Other                                                       16,230           16,230
                                                           ----------       ----------
                                                              491,551          506,817  
                                                           ----------       ----------
Property, Plant & Equipment
   Oil & Gas Properties, at Cost Based on the
      Successful Efforts Method of Accounting
           Unproved Properties                                629,689          597,284
           Proved Properties                                4,268,694        4,228,063
                                                           ----------       ----------
                                                            4,898,383        4,825,347
      Less - Valuation Allowance and Accumulated
           Depreciation, Depletion & Amortization           3,454,538        3,427,157
                                                           ----------       ----------
                                                            1,443,845        1,398,190
                                                           ----------       ----------
    Other Property & Equipment, at Cost                       324,104          324,104
      Less - Accumulated Depreciation & Amortization          171,695          169,195
                                                           ----------       ----------
                                                              152,409          154,909
                                                           ----------       ----------
                                                            1,596,254        1,553,099
                                                           ----------       ----------
Other Assets                                                  483,452          478,137
                                                           ----------       ----------
                                                           $7,069,726       $6,965,389
                                                           ==========       ==========


</TABLE>                                                  
(continued)
See Accompanying Notes


                                       3
<PAGE>   4


                         THE RESERVE PETROLEUM COMPANY
                                 BALANCE SHEETS
                                  (Unaudited)


(Concluded)



                      LIABILITIES AND STOCKHOLDERS' EQUITY


<TABLE>
<CAPTION>
                                                  March 31,         December 31,
                                                    1997                1997 
                                                 ------------       ------------
<S>                                              <C>                <C>         
Current Liabilities:
   Accounts Payable                              $     56,416       $     93,044
   Other Current Liabilities
      Gas Balancing Commitment                         45,344             45,344
       Other                                           13,741             13,741
                                                 ------------       ------------
                                                      115,501            152,129
                                                 ------------       ------------

Dividends Payable                                     131,658            132,094
                                                 ------------       ------------
Commitments & Contingencies

Stockholders' Equity
   Common Stock                                        92,368             92,368
   Additional Paid-in Capital                          65,000             65,000
   Retained Earnings                                6,840,914          6,698,773
                                                 ------------       ------------
                                                    6,998,282          6,856,141

   Less  - Treasury Stock at Cost                     175,715            174,975
                                                 ------------       ------------
                                                    6,822,567          6,681,166
                                                 ------------       ------------
                                                 $  7,069,726       $  6,965,389
                                                 ============       ============
</TABLE>


See Accompanying Notes




                                       4
<PAGE>   5

                         THE RESERVE PETROLEUM COMPANY
                            STATEMENTS OF OPERATIONS
                                  (Unaudited)


   
<TABLE>
<CAPTION>
                                                      Three Months Ended
                                                            March 31,              
                                                -------------------------------
                                                    1998               1997 
                                                ------------       ------------
<S>                                             <C>                <C>         
Operating Revenues:
    Oil and Gas Sales                           $    500,572       $    952,408
    Lease Bonuses and Other                              848              3,294
                                                ------------       ------------
                                                     501,420            955,702
                                                ------------       ------------
Operating Costs and Expenses:
    Production                                        89,987             93,814
    Exploration                                       28,842             51,141
    Depreciation, Depletion, Amortization
         and Valuation Provisions                     69,147             91,223
    General, Administrative and Other                177,208            193,236
                                                ------------       ------------
                                                     365,184            429,414
                                                ------------       ------------
Income  from Operations                              136,236            526,288
Other Income, Net                                     58,827             30,906
                                                ------------       ------------
Income  Before Income Taxes                          195,063            557,194
Provision for
    Income Taxes                                      52,923            141,700
                                                ------------       ------------
Net Income                                      $    142,140       $    415,494
                                                ============       ============
Per Share Data
    Net Income, Basic and Diluted               $        .84       $       2.47
                                                ============       ============
    

    Weighted Average Shares
         Outstanding, Basic and Diluted              168,310            168,466
                                                ============       ============
</TABLE>


See Accompanying Notes




                                       5
<PAGE>   6
                         THE RESERVE PETROLEUM COMPANY
                            STATEMENTS OF CASH FLOW
                                  (Unaudited)
                Increase (Decrease) in Cash and Cash Equivalents


<TABLE>
<CAPTION>
                                                            Three Months Ended
                                                                 March 31,               
                                                     --------------------------------
                                                        1998                1997 
                                                     ------------        ------------
<S>                                                  <C>                 <C>         
Net Cash Provided by Operating Activities            $    224,637        $    495,410
                                                     ------------        ------------
Cash Flows from Investing Activities:
    Sale and Maturity of Available
      for Sale Securities                                      --             276,928
    Purchase of Available for Sale Securities            (287,578)           (592,295)
    Property Dispositions                                     837              18,426
    Property Additions                                   (150,373)           (182,598)
    Cash Distributions from Equity Investments             13,500              19,500
                                                     ------------        ------------
    Net Cash Applied to Investing Activities             (423,614)           (460,039)
                                                     ------------        ------------
Cash Flows from Financing Activities:
    Decrease in Dividends Payable                            (435)             (2,081)
    Purchase of Treasury Stock                               (740)               (560)
                                                     ------------        ------------
    Cash Applied to Financing Activities                   (1,175)             (2,641)
                                                     ------------        ------------
Net Change in Cash and Cash Equivalents                  (200,152)             32,730
Cash and Cash Equivalents,
    Beginning Period                                      313,540             385,136
                                                     ------------        ------------
Cash and Cash Equivalents,
    End of Period                                    $    113,388        $    417,866
                                                     ============        ============
Supplemental Disclosures of
    Cash Flow Information,
      Cash Paid During the Periods for:
           Interest                                  $      3,750        $      3,750
           Income Taxes                              $         --        $    190,000
</TABLE>



See Accompanying Notes




                                       6
<PAGE>   7

                         THE RESERVE PETROLEUM COMPANY
                    NOTES TO CONDENSED FINANCIAL STATEMENTS
                                 March 31, 1998
                                  (Unaudited)


 Note 1 - ADJUSTMENTS

          In the opinion of Management, the accompanying financial statements
          reflect all adjustments which are necessary for a fair statement of
          the results of the interim periods presented.

 Note 2 - MATERIAL CONTINGENCIES

          In August 1993, the Company filed an action in the District Court of
          Leon County, Texas to quiet title to its 13/32nd interest in
          approximately 203 mineral acres associated with two producing oil and
          gas wells completed in 1988.   Following a jury trial held in August,
          1996, a judgment was entered in favor of the Company on all its
          claims. Certain defendants appealed the judgment to the Texas Court
          of Appeals.  On February 11, 1998, the appellate court affirmed the
          judgment in all respects as to the issues affecting the Company's
          mineral interests, but denied recovery of attorney's fees awarded by
          the trial court.  On April  1, 1998, one defendant filed a petition
          for review in the Supreme Court of the State of Texas.  Approximately
          $854,000 of proceeds from oil and gas sales are held in suspense by
          the unit operator.  These proceeds will be recorded as revenue by the
          Company when released by the unit operator.  The Company has expended
          approximately $448,500 in drilling, completion and operating costs
          for these wells of which $195,422 was included in the Company's net
          investment in oil and gas properties at March 31, 1998.

          An action was filed in the District Court of Robertson County, Texas,
          seeking a declaration that the Plaintiff owns an additional interest
          in the Brounkowski Gas Unit.  The  Company was added as a Defendant
          in this action in December, 1997, because it owns minerals included
          in the Brounkowski Unit.  Plaintiff does not assert claims directly
          against the Company and the information available to the Company at
          this time appears to indicate that if the Plaintiff were successful
          in this action, the minerals he claims are currently in the name of
          parties other than the Company.  In February, 1998, the operator
          suspended payment of proceeds from gas sales after filing of
          Plaintiff's amended petition.  The Company's management is taking
          steps to obtain current payments from the operator and believe the
          long-term suspension, if any, will not exceed 10% of the Company's
          interest in production, or approximately $3,500 per month.  The
          Company has recorded an estimated 90% of the suspended proceeds as
          oil and gas sales for the quarter ended March 31, 1998.  As a result,
          oil and gas sales were increased by $100,350 and net income was
          increased by $60,009 ($.36 per share).




                                       7
<PAGE>   8

                         THE RESERVE PETROLEUM COMPANY
                      MANAGEMENT'S DISCUSSION AND ANALYSIS
                OF FINANCIAL CONDITION AND RESULTS OF OPERATIONS
                                 March 31, 1998
                                  (Unaudited)


    The discussion and analysis of financial condition and results of
    operations should be read with reference to the Company's December 31,
    1997, Form 10-KSB filed with the Securities and Exchange Commission, as
    well as the condensed financial statements included in this Form
    10-QSB.

1.  Liquidity and Capital Resources.

    The Company's net working capital at March 31, 1998, was $4,382,968, an
    amount which, along with the cash flow from operations, is adequate to fund
    all currently budgeted investing and financing activities.

    For the quarter ended March 31, 1998, cash flows from operations declined
    $270,773 (55%) to $224,637 from $495,410 for the quarter ended March 31,
    1997.  To a great extent, the decline was the result of falling prices
    received for the Company's  crude oil and natural gas sales as well as
    suspended payment of proceeds from a natural gas royalty interest.  See
    Note 2, to the accompanying Condensed Financial Statements for a discussion
    of the suspended payments. Management is unaware of any  additional
    material trends, demands, commitments, events or uncertainties which would
    impact liquidity and capital resources to the extent that the discussion
    presented in Form 10-KSB for December 31, 1997, would not be representative
    of the Company's current position.

 2. Material Changes in Results of Operations Three  Months Ended March 31,
    1998 Compared with Three Months Ended March 31, 1997.

    Oil and gas sales decreased $451,836 (47%) to $500,572 as a result of a
    decline in both price and volume.  Revenues from oil sales fell $99,203
    (42%) to $140,001.  The volume of oil sales declined 1,490 barrels (Bbls)
    to 9,238 Bbls resulting in a negative volume variance of $33,227.  The
    average price received for oil sales fell $7.14 per Bbl to $15.16 per Bbl
    resulting in a negative price variance of $66,000.  At May 5, 1998, the
    Oklahoma State spot market for Oklahoma sweet and West Texas intermediate
    crude oil was $13 per Bbl.  Management anticipates the depressed prices
    will prevail through the second quarter, at a minimum.

    Revenues from  natural gas sales declined $352,294 (48%) to $356,315 in
    1998 from $708,609 in 1997.  The average price per thousand cubic feet
    (MCF) fell $.99 from $3.18 per MCF in 1997 to $2.19 per MCF in 1998,
    resulting in a negative price variance of $160,540.  The volume of gas sold
    decreased 60,300 MCF (25%) from 222,607 MCF in 1997 to 162,307 MCF in 1998.
    Of the net decrease in volume of 60,300 MCF, a decline in production of a
    Robertson County, Texas royalty interest accounted for 50,102 (83%) of
    the decline as well as $119,062 (34%) of the total $352,294 decrease in gas
    sales.  See Note 2 to the accompanying Condensed Financial Statements,
    which provide information regarding the operator's suspension of gas runs
    from the Texas royalty interest.





                                       8
<PAGE>   9

                                    PART II

                               OTHER INFORMATION


Item 6.   Exhibits and Reports on Form 8-K.

     (a)  Exhibit 27.  Financial Data Schedule.

     (b)  No reports on Form 8-K were required to be filed by the Registrant for
          the three months ended March 31, 1998.



                                   SIGNATURES


Pursuant to the requirements of the Securities Exchange Act of 1934, the
Registrant has duly caused this report to be signed on its behalf by the
undersigned thereto duly authorized.





                                     THE RESERVE PETROLEUM COMPANY
                                     -----------------------------
                                     (Registrant)





Date: May  8, 1998                   /s/ Mason McLain                         
     ---------------                 ------------------------------------------
                                     Mason McLain,
                                     President





Date:  May   8, 1998                 /s/  Jerry L. Crow                       
     ---------------                 ------------------------------------------
                                     Jerry L. Crow
                                     Principal Financial and Accounting Officer




                                       9
<PAGE>   10

                               INDEX TO EXHIBITS

<TABLE>
<CAPTION>
EXHIBIT
NUMBER       DESCRIPTION
------       -----------
<S>          <C>
27           Financial Data Schedule
</TABLE>