<PAGE>   1
                       SECURITIES AND EXCHANGE COMMISSION

                             Washington, D.C. 20549

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

                                    FORM 10-Q

(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
                               --------------


                                       OR

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

For the transition period from                to
                               --------------    -------------

                          Commission File Number 1-4014

                                   FINA, Inc.
             (Exact name of registrant as specified in its charter)

                   Delaware                               13-1820692
        (State or other jurisdiction of                (I.R.S. Employer
        incorporation or organization)                Identification No.)

           Fina Plaza, Dallas, Texas                         75206
   (Address of principal executive offices)               (Zip Code)

        Registrant's telephone number, including area code (214) 750-2400
                                                           --------------

Indicate by check mark whether the registrant (1) has 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 over the past 90 days.

                                    Yes X No

                      APPLICABLE ONLY TO CORPORATE ISSUERS:

Indicate the number of shares outstanding of each of the issuer's classes of
common stock, as of the latest practicable date.

                     29,247,172 Class A as of April 27, 1998
                      2,000,000 Class B as of April 27, 1998


<PAGE>   2


                           FINA, INC. AND SUBSIDIARIES
                      CONDENSED CONSOLIDATED BALANCE SHEETS
               (IN THOUSANDS, EXCEPT SHARE AND PER SHARE AMOUNTS)
                                   (UNAUDITED)

<TABLE>
<CAPTION>
                                                                             MARCH 31,      DECEMBER 31,
                                                                               1998             1997
                                                                           ------------     ------------
<S>                                                                        <C>              <C>         
ASSETS
Current assets:
   Cash and cash equivalents                                               $      2,563     $      1,271
   Accounts and notes receivable                                                564,175          581,724
   Inventories                                                                  313,036          345,235
   Prepaid expenses and other current assets                                     47,040           47,732
                                                                           ------------     ------------
            Total current assets                                                926,814          975,962
                                                                           ------------     ------------

Property, plant, and equipment; net of $1,667,501 accumulated
  depreciation at 3/31/98 and $1,633,688 at 12/31/97                          1,831,396        1,849,378
Other assets                                                                    207,399          189,334
                                                                           ------------     ------------
                                                                           $  2,965,609     $  3,014,674
                                                                           ============     ============

LIABILITIES AND STOCKHOLDERS' EQUITY
Current liabilities:
   Short term obligations                                                  $    149,390     $     27,478
   Current installments of long term debt and lease obligations                  61,363           63,860
   Accounts payable and accrued liabilities                                     585,680          735,609
                                                                           ------------     ------------
            Total current liabilities                                           796,433          826,947
                                                                           ------------     ------------

Long term debt, excluding current installments                                  593,261          594,988
Other deferred credits and liabilities                                          313,182          315,627
Stockholders' equity:
   Preferred stock of $1 par value. Authorized 4,000,000 shares;
      none issued                                                                    --               --
   Class A common stock of $.50 par value. Authorized
      38,000,000 shares; issued and outstanding 29,238,572 and
      29,221,972 shares in 1998 and 1997                                         14,619           14,611
   Class B common stock of $.50 par value. Authorized
      and issued 2,000,000 shares                                                 1,000            1,000
   Additional paid-in capital                                                   451,677          451,100
   Retained earnings                                                            795,437          810,401
                                                                           ------------     ------------
            Total stockholders' equity                                        1,262,733        1,277,112

Commitments and contingencies                                                        --               --
                                                                           ------------     ------------
                                                                           $  2,965,609     $  3,014,674
                                                                           ============     ============
</TABLE>



See accompanying notes to consolidated financial statements.


<PAGE>   3


                           FINA, INC. AND SUBSIDIARIES
                       CONSOLIDATED STATEMENTS OF EARNINGS
                    (IN THOUSANDS, EXCEPT PER SHARE AMOUNTS)
                                   (UNAUDITED)



<TABLE>
<CAPTION>
                                                         THREE MONTHS ENDED MARCH 31,
                                                         -----------------------------
                                                             1998             1997
                                                         ------------     ------------
<S>                                                      <C>              <C>         
Revenues:
   Sales and other operating revenues                    $  1,018,009     $  1,114,068
   Interest and other, net                                     20,194            5,375
                                                         ------------     ------------

                                                            1,038,203        1,119,443
                                                         ------------     ------------

Costs and expenses:
   Cost of raw materials and products purchased               838,794          878,116
   Direct operating expenses                                   87,770           87,927
   Selling, general, and administrative expenses               23,395           21,427
   Taxes, other than on income                                 14,687           14,351
   Dry holes and abandonments                                     580            2,055
   Depreciation, depletion, amortization,
     and lease impairment                                      48,729           47,478
   Interest charges, net                                        8,863            9,605
                                                         ------------     ------------

                                                            1,022,818        1,060,959
                                                         ------------     ------------

Earnings before income taxes                                   15,385           58,484
Income taxes                                                    5,363           19,334
                                                         ------------     ------------

            Net earnings                                 $     10,022     $     39,150
                                                         ============     ============

Basic and diluted earnings per common share (note 2)     $       0.32     $       1.25
                                                         ============     ============
</TABLE>



See accompanying notes to consolidated financial statements.

<PAGE>   4

                           FINA, INC. AND SUBSIDIARIES
                      CONSOLIDATED STATEMENTS OF CASH FLOWS
                   THREE MONTHS ENDED MARCH 31, 1998 AND 1997
                                 (IN THOUSANDS)
                                   (UNAUDITED)

<TABLE>
<CAPTION>
                                                                              1998           1997
                                                                           ---------      ---------
<S>                                                                        <C>            <C>      
Cash flows from operating activities:
   Net earnings                                                            $  10,022      $  39,150
   Adjustments to reconcile net earnings to net cash
      provided by operating activities:
      Depreciation, depletion, amort., lease impairment & abandonments        48,852         47,584
      Net equity in losses of affiliates                                       1,966          1,605
      Gain on sale of assets                                                 (22,051)        (6,176)
      Changes in assets and liabilities:
          Accounts and notes receivable                                       17,549         (5,038)
          Inventories                                                         32,199          9,430
          Prepaid expenses and other current assets                              692         (1,004)
          Accounts payable and accrued liabilities                          (154,609)       (45,959)
          Current and deferred income taxes                                    6,286          9,967
          Other                                                              (25,216)        (2,143)
                                                                           ---------      ---------

             Net cash provided by (used in) operating activities             (84,310)        47,416
                                                                           ---------      ---------

Cash flows from investing activities:
   Additions to property, plant and equipment                                (41,992)       (24,744)
   Proceeds from sale of assets                                               34,854          8,424
   Investments in and advances to affiliates                                    (547)        (2,009)
                                                                           ---------      ---------

             Net cash used in investing activities                            (7,685)       (18,329)
                                                                           ---------      ---------

Cash flows from financing activities:
   Additions to long term debt and lease obligations                               0             18
   Payments of long term debt and lease obligations                           (4,224)        (3,840)
   Net change in short term obligations                                      121,912          3,123
   Issuance of common stock                                                      585             35
   Dividends paid                                                            (24,986)       (21,852)
                                                                           ---------      ---------

             Net cash provided by (used in) financing activities              93,287        (22,516)
                                                                           ---------      ---------

Net increase in cash and cash equivalents                                      1,292          6,571
Cash and cash equivalents at beginning of year                                 1,271          1,585
                                                                           ---------      ---------

Cash and cash equivalents at end of period                                 $   2,563      $   8,156
                                                                           =========      =========
</TABLE>





<PAGE>   5


                           FINA, INC. AND SUBSIDIARIES
                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS
                                 MARCH 31, 1998
                                   (UNAUDITED)

(1)   The information furnished reflects all adjustments which are, in the
      opinion of management, necessary to a fair presentation of the results of
      the interim periods presented. The results of operations for the three
      months ended March 31, 1998 are not necessarily indicative of the
      operating results for the full fiscal year.

(2)   Basic earnings per share (EPS) is computed by dividing income available to
      common shareholders by the weighted-average number of common shares
      outstanding for the period. Diluted EPS reflects the potential dilution
      that could occur if securities or other contracts to issue common stock
      were exercised or converted into common stock or resulted in the issuance
      of common stock that then shared in the earnings of the entity. For the
      periods presented herein, basic and diluted EPS are the same. The weighted
      average number of outstanding common shares was 31,228,872 and 31,216,722
      for the three months ended March 31, 1998 and 1997, respectively.

(3)   The Company is contingently liable under pending lawsuits and other
      claims, some of which involve substantial sums. Considering certain
      liabilities which have been set up for the lawsuits and claims, and the
      difficulty in determining the ultimate liability in some of these matters,
      internal counsel is of the opinion that the amounts, if any, which
      ultimately might be due in connection with such lawsuits and claims would
      not have a material adverse effect upon the Company's consolidated
      financial condition.

(4)   The notes to the consolidated financial statements on pages 19 through 35
      of the Company's 1997 Form 10-K are an integral part of these consolidated
      financial statements.

(5)   Fina Oil and Chemical Company ("FOCC"), a wholly-owned subsidiary of FINA,
      Inc., is the main operating subsidiary of the Company whose principal
      lines of business include crude oil and natural gas exploration and
      production; petroleum products refining, supply and transportation and
      marketing; and chemicals manufacturing and marketing. Following is summary
      consolidated financial data for FOCC (in thousands):

<TABLE>
<CAPTION>
                                                March 31,       December 31, 
                                                   1998              1997 
                                              ------------      ------------ 
<S>                                           <C>               <C>          
      Current assets                          $    777,380      $    846,240 
      Noncurrent assets                          2,001,347         2,296,640 
      Current liabilities                         (654,633)         (704,163)
      Noncurrent liabilities (1)                (1,994,736)       (2,318,492)
                                              ------------      ------------
                 Net Assets                   $    129,358      $    120,225 
                                              ============      ============
</TABLE>


<TABLE>
<CAPTION>
                                               Three Months Ended March 31,
                                                  1998             1997
                                              ------------     ------------
<S>                                           <C>              <C>         
      Sales and other operating revenues      $    684,868     $    960,099
                                              ============     ============
      Gross profit (2)                        $     28,246     $     82,608
                                              ============     ============
      Net earnings                            $      9,383     $     37,184
                                              ============     ============
</TABLE>

      (1) Primarily consists of payables to related parties.

      (2) Gross profit is defined as sales and other operating revenues less
      cost of raw materials and products purchased; direct operating expenses;
      taxes, other than on income; and depreciation, depletion, amortization and
      lease impairment.

<PAGE>   6


Notes continued:

(6)   Effective January 1, 1998, the Company adopted Statement of Financial
      Accounting Standards ("SFAS") No. 130 "Reporting Comprehensive Income."
      SFAS No. 130 establishes standards for reporting and display of
      comprehensive income in a full set of general-purpose financial
      statements. Comprehensive income includes net income and other
      comprehensive income which is generally comprised of changes in the fair
      value of available-for-sale marketable securities, foreign currency
      translation adjustments and adjustments to recognize additional minimum
      pension liabilities. The Company had no accumulated other comprehensive
      income at December 31, 1997 and no comprehensive income for three months
      ended March 31, 1998 and 1997.

(7)   Because of price declines in a majority of the products during the three
      months ended March 31, 1998, inventory was reduced by $41 million to net
      realizable value.


<PAGE>   7
                           FINA, INC. AND SUBSIDIARIES
                          UNAUDITED SEGMENT INFORMATION

<TABLE>
<CAPTION>
                                                                      ------------------------------
                                                                              FIRST QUARTER
                                                                          1998              1997
                                                                      ------------      ------------
 EARNINGS      (Thousands, except share and per-share amounts)
 --------
<S>                                                                   <C>               <C>         
        Upstream                                                      $     28,037      $     35,487
        Downstream                                                           1,127             2,007
        Chemicals                                                           (1,681)           35,074
        Corporate / Financing                                              (12,098)          (14,084)
        Income Tax                                                          (5,363)          (19,334)
                                                                      ------------      ------------
           Total Net Earnings                                         $     10,022      $     39,150
                                                                      ============      ============
           Net Earnings Per Share                                     $       0.32      $       1.25
                                                                      ============      ============
           Average Shares Outstanding                                   31,228,872        31,216,722

 OPERATING STATISTICS
 --------------------
    Upstream
        Crude Oil Production - MBD                                            10.3              10.3
        Natural Gas Production - MMCFD                                         180               189
        Natural Gas Sales - MMCFD                                            1,412               727
        Average Oil Price/BBL                                         $      12.97      $      20.34
        Average Natural Gas Sales Price/MCF                           $       2.42      $       2.91

    Downstream
        Refinery Throughput - MBD                                            222.0             232.2

    Chemicals
        Sales Volume - MMLB                                                1,013.6           1,000.4
</TABLE>





<PAGE>   8
                                 PART I - Item 2

MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND RESULTS OF
OPERATIONS.

         Net earnings were $10,022,000 for the quarter ended March 31, 1998
compared to $39,150,000 for the first quarter of 1997. Sales and other operating
revenues were $1,018,009,000 compared to $1,114,068,000 for first quarter 1997.
Earnings per share were $0.32 compared to $1.25 per share for the first quarter
of last year.

         The net earnings decrease in first quarter 1998 was largely
attributable to a non-cash LIFO inventory write-down of $27 million after tax
due to the drop in crude oil and product prices, only partially offset by an
asset sale of 50% of the Company's interest in undeveloped Gulf of Mexico
properties. Sales and other operating revenues decreased 9% from the same period
last year, with lower prices in all segments partially offset by higher natural
gas sales volumes. Excluding unusual items, first quarter net income would have
been $25.2 million.

         First quarter capital expenditures of $42.3 million, largely for two
major chemicals expansion projects, exploration and development drilling and the
FINA-Holly Pipeline project, increased 54% compared to the same period last
year.

         Total debt, including Cos-Mar debt guaranteed by the Company, at the
end of the first quarter was $854 million, with a debt to capital ratio of 40.3%
compared to 36.6% at year-end 1997. This increase is principally due to reduced
cash flows from operations and a larger capital expansion program. A debt
management program is being implemented to increase cash flows from operations,
reduce costs and generate proceeds from asset sales.

         In the Upstream, earnings before interest and income taxes (EBIT) was
$28,037,000 in the first quarter of 1998 compared to $35,487,000 for the same
period in 1997. This decrease reflects a 23% decrease in natural gas wellhead
prices, a 36% decrease in crude wellhead prices, and a 5% decrease in natural
gas production volume, only partially offset by asset sales gains. Total natural
gas sales increased 94% to 1.4 billion cubic feet per day. The debt management
program includes asset divestitures and trades and concentration on development
of core properties which are expected to significantly improve the Upstream's
financial results and generate cash. This plan included the sale of 50% of the
Company's interest in Gulf of Mexico undeveloped properties which has been
completed.

         In the Downstream, earnings before interest and income taxes (EBIT)
decreased to $1,127,000 in the first quarter of 1998 compared to $2,007,000 for
the same period in 1997. The primary factors contributing to the decrease were
the LIFO write-down and the Crude Unit maintenance and upgrade work at the Big
Spring, Texas Refinery. Combined throughput for both refineries was 222,000
barrels per day. As a result of the Crude Unit upgrades, the Big Spring Refinery
is now able to increase throughput by 7%, which will allow better utilization of
the increased product outlet capabilities following start-up of the FINA-Holly
Pipeline project in summer 1998. The Company is continuing to develop its
partnership with BASF to build the world's largest steam cracker unit and
related facilities at the Port Arthur, Texas Refinery. The project is still
subject to final Board approvals of both companies.

         Chemicals EBIT for the first quarter was a loss of $1,681,000 which was
a decrease from first quarter 1997's EBIT of $35,074,000 mainly due to a $35
million before tax LIFO inventory write-down. Margins improved during the
quarter so that the average was very close to the same period last year. Total
sales volumes increased slightly to 1,013.6 million pounds. Capacity at the La
Porte, Texas Polypropylene Plant, already the world's largest, will be increased
to 2,150 million pounds per year, while the Bayport, Texas Polyethylene Plant
will double in size to 850 million pounds per year. Start-up of these expansions
is anticipated later this year.

         The Company's annual meeting of shareholders was held April 15, 1998.
All members of the Board of Directors as proposed in the Company's Proxy
Statement were elected.
<PAGE>   9

         The Company's regular quarterly dividend of $.80 per share was paid on
March 18, 1998 to shareholders of record on March 6, 1998. On April 23, 1998,
the Board of Directors voted a regular quarterly dividend of $.80 per share to
be paid on June 15, 1998 to shareholders of record on June 3, 1998.



<PAGE>   10



                           Part II - OTHER INFORMATION

Item 1. Legal Proceedings.

         Not Applicable

Item 2. Changes in Securities.

         (a)  Not Applicable

         (b)  Not Applicable

Item 3. Defaults upon Senior Securities.

         Not Applicable

Item 4. Submission of Matters to a Vote of Security Holders.

         At the annual meeting of shareholders held April 15, 1998 nine
directors were elected.

Item 5. Other Information.

         Not Applicable

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

         A Form 8-K was filed on February 17, 1998 reporting a news release
         by the Company approving PetroFina S.A.'s offer of a negotiated
         merger whereby the Company would become an indirect, wholly-owned
         affiliate. Full disclosure was made in the Company's Form 10-K about
         the proposed merger.

         Exhibits incorporated herein by reference:

         (10j)     Agreement between the Company  and Neil A. Smoak

         (27)      Financial Data Schedule



<PAGE>   11



                                   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 thereunto duly authorized.

                                        FINA, Inc.
                                        -------------------------------
                                        (REGISTRANT)

Date: May 12, 1998

                                        BY:
                                        Geoffroy Petit
                                        Vice President and Chief  
                                        Financial Officer


<PAGE>   12

                                INDEX TO EXHIBITS

<TABLE>
<CAPTION>
EXHIBIT
NUMBER       DESCRIPTION
------       -----------
 <S>         <C>                                                     
 10.j        Agreement between the Company and Neil A. Smoak
 27          Financial Data Schedule
</TABLE>