<PAGE>   1
 
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                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549
 
                                   FORM 10-Q
 
            QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(D) OF THE
                        SECURITIES EXCHANGE ACT OF 1934
                  FOR THE QUARTERLY PERIOD ENDED JUNE 30, 1997
                         COMMISSION FILE NUMBER 1-7521
 
                       FRIEDMAN INDUSTRIES, INCORPORATED
             (Exact name of registrant as specified in its charter)
 
<TABLE>
<S>                                            <C>
                    TEXAS                                             74-1504405
       (State or other jurisdiction of                     (I.R.S. Employer Identification
        incorporation or organization)                                 Number)
</TABLE>
 
                 4001 HOMESTEAD ROAD, HOUSTON, TEXAS 77028-5585
                (Address of principal executive office zip code)
       Registrant's telephone number, including area code (713) 672-9433
 
--------------------------------------------------------------------------------
Former name, former address and former fiscal year, of changed since last report
 
     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, and (2) has been subject to such filing
requirements for the past 90 days.
 
                               Yes  X     No
 
     At June 30, 1997, the number of shares outstanding of the issuer's only
class of stock was 6,469,731 shares of Common Stock.
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<PAGE>   2
 
                        PART I -- FINANCIAL INFORMATION
 
                       FRIEDMAN INDUSTRIES, INCORPORATED
                    CONSOLIDATED BALANCE SHEETS -- UNAUDITED
 
                                     ASSETS
 
<TABLE>
<CAPTION>
                                                              JUNE 30, 1997    MARCH 31, 1997
                                                              -------------    --------------
<S>                                                           <C>              <C>
CURRENT ASSETS
  Cash and cash equivalents.................................  $     544,906    $      168,245
  Accounts receivable, less allowance for doubtful accounts
     ($7,276 at June 30, 1997 and March 31, 1997,
     respectively)..........................................     13,630,363        11,902,925
  Inventories -- Note B.....................................     23,460,314        21,203,665
  Prepaid expenses and other current assets.................        149,135            82,325
                                                              -------------    --------------
          Total Current Assets..............................     37,784,718        33,357,160
PROPERTY, PLANT AND EQUIPMENT
  Land......................................................        198,021           198,021
  Buildings and improvements................................      2,727,449         2,695,913
  Machinery and equipment...................................     11,900,012        11,724,974
  Less allowance for depreciation...........................     (9,968,977)       (9,909,444)
                                                              -------------    --------------
                                                                  4,856,505         4,709,464
OTHER ASSETS
  Cash value of officers' life insurance....................         57,486            50,567
                                                              -------------    --------------
                                                              $  42,698,709    $   38,117,191
                                                              =============    ==============
 
LIABILITIES AND STOCKHOLDERS' EQUITY
 
CURRENT LIABILITIES
  Trade accounts payable and accrued expenses...............  $  11,736,636    $    8,112,096
  Current portion of long-term debt.........................        800,000           800,000
  Dividends payable.........................................        453,296           369,715
  Contribution to profit-sharing plan.......................         62,499           242,000
  Federal income taxes payable..............................        632,698           256,434
  Employee compensation and related expenses................        562,655           392,427
                                                              -------------    --------------
          Total Current Liabilities.........................     14,247,784        10,172,672
LONG-TERM DEBT, less current portion........................      4,400,000         4,600,000
PROVISION FOR NONPENSION RETIREMENT BENEFITS................        113,000           113,000
DEFERRED INCOME TAXES.......................................        434,560           449,560
STOCKHOLDERS' EQUITY
Common stock:
  Par value $1 per share:
     Authorized 10,000,000 shares; Issued and outstanding
       shares -- 6,469,731 at June 30, 1997 and 6,161,994 at
       March 31, 1997.......................................      6,469,731         6,161,994
  Additional paid-in capital................................     23,646,661        22,377,246
  Retained earnings.........................................     (6,613,027)       (5,757,281)
                                                              -------------    --------------
          Total Stockholders' Equity........................     23,503,365        22,781,959
                                                              -------------    --------------
                                                              $  42,698,709    $   38,117,191
                                                              =============    ==============
</TABLE>
 
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<PAGE>   3
 
                       FRIEDMAN INDUSTRIES, INCORPORATED
 
                CONSOLIDATED STATEMENT OF EARNINGS -- UNAUDITED
 
<TABLE>
<CAPTION>
                                                              THREE MONTHS ENDED JUNE 30,
                                                              ----------------------------
                                                                  1997            1996
                                                              ------------    ------------
<S>                                                           <C>             <C>
Net sales...................................................   $38,300,432     $28,751,479
Costs and expenses
  Costs of goods sold.......................................    35,065,621      26,128,966
  General, selling and administrative costs.................     1,353,728       1,106,965
  Interest..................................................       115,588         134,223
                                                               -----------     -----------
                                                                36,534,937      27,370,154
Interest and other income...................................       (17,179)        (28,996)
                                                               -----------     -----------
Earnings before federal income taxes........................     1,782,674       1,410,321
Provision (benefit) for federal income taxes:
  Current...................................................       621,110         492,009
  Deferred..................................................       (15,000)        (12,500)
                                                               -----------     -----------
                                                                   606,110         479,509
                                                               -----------     -----------
Net earnings................................................   $ 1,176,564     $   930,812
                                                               ===========     ===========
Net earnings per share -- Note C............................   $      0.18     $      0.14
                                                               ===========     ===========
Cash dividends declared per common share....................   $      0.07     $      0.05
                                                               ===========     ===========
</TABLE>
 
                                        2
<PAGE>   4
 
                       FRIEDMAN INDUSTRIES, INCORPORATED
 
               CONSOLIDATED STATEMENTS OF CASH FLOWS -- UNAUDITED
 
<TABLE>
<CAPTION>
                                                              THREE MONTHS ENDED JUNE 30,
                                                              ----------------------------
                                                                  1997            1996
                                                              ------------    ------------
<S>                                                           <C>             <C>
OPERATING ACTIVITIES
  Net earnings..............................................   $ 1,176,564     $   930,812
  Adjustments to reconcile net income to cash provided by
     operating activities:
     Depreciation...........................................       166,026         158,010
     Provision for deferred taxes...........................       (15,000)        (12,500)
  Decrease (increase) in operating assets:
     Accounts receivable....................................    (1,727,438)       (400,908)
     Inventories............................................    (2,256,649)     (1,310,491)
     Other current assets...................................       (66,810)        (81,069)
  Increase (decrease) in operating liabilities:
     Accounts payable and accrued expenses..................     3,624,540         730,941
     Contribution to profit-sharing plan payable............      (179,501)       (162,000)
     Employee compensation and related expenses.............       170,228          56,827
     Federal income taxes payable...........................       376,264          42,009
                                                               -----------     -----------
NET CASH PROVIDED (USED) BY OPERATING ACTIVITIES............     1,268,224         (48,369)
INVESTING ACTIVITIES
  Purchase of property, plant and equipment.................      (313,069)         (3,691)
  Increase in cash surrender value of officers' life
     insurance..............................................        (6,919)        (23,828)
                                                               -----------     -----------
          NET CASH USED IN INVESTING ACTIVITIES.............      (319,988)        (27,519)
FINANCING ACTIVITIES
  Cash dividends paid.......................................      (371,575)       (293,303)
  Principal payments on long-term debt......................      (200,000)       (200,000)
                                                               -----------     -----------
          NET CASH PROVIDED (USED) IN FINANCING
             ACTIVITIES.....................................      (571,575)       (493,303)
                                                               -----------     -----------
INCREASE (DECREASE) IN CASH AND CASH EQUIVALENTS............       376,661        (569,191)
  Cash and cash equivalents at beginning of period..........       168,245         595,216
                                                               -----------     -----------
CASH AND CASH EQUIVALENTS AT END OF PERIOD..................   $   544,906     $    26,025
                                                               ===========     ===========
</TABLE>
 
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<PAGE>   5
 
                       FRIEDMAN INDUSTRIES, INCORPORATED
 
                     NOTES TO QUARTERLY REPORT -- UNAUDITED
                        THREE MONTHS ENDED JUNE 30, 1997
 
NOTE A -- BASIS OF PRESENTATION
 
     The accompanying unaudited condensed, consolidated financial statements
have been prepared in accordance with the instructions to Form 10-Q and do not
include all of the information and footnotes required by generally accepted
accounting principles for complete financial statements. In the opinion of
management, all adjustments (consisting of normal recurring accruals) considered
necessary for a fair presentation have been included. For further information
refer to the financial statements and footnotes included in the Company's annual
report on Form 10-K for the year ended March 31, 1997.
 
NOTE B -- INVENTORIES
 
     Coil inventory consists primarily of raw materials. Tubular inventory is
comprised of both raw materials and finished goods.
 
NOTE C -- EARNINGS PER SHARE
 
     Earnings per common and common equivalent share for the periods ended June
30, 1997 and June 30, 1996 are based on the weighted average number of common
and common equivalent (stock options) shares outstanding as follows:
 
<TABLE>
<CAPTION>
                                                                1997         1996
                                                              ---------    ---------
<S>                                                           <C>          <C>
Common Stock:
  Shares outstanding during the entire period...............  6,161,994    5,834,195
  Retroactive effect of stock dividends declared............    307,737      597,593
                                                              ---------    ---------
          Weighted average number of common and common
            equivalent shares...............................  6,469,731    6,431,788
                                                              =========    =========
</TABLE>
 
     Earnings per share assuming full dilution for the quarters ended June 30,
1997 and 1996, are not presented because they are not materially dilutive. Stock
options are not included in the above computations of common and common
equivalent shares outstanding since their effect is not significant.
 
     In February 1997, the Financial Accounting Standards Board issued Statement
of Financial Accounting Standards No. 128, Earnings Per Share, which is required
to be adopted for financial statements issued for periods ending after December
31, 1997. The statement replaces primary and fully diluted earnings per share
with basic and diluted earnings per share. The Company does not anticipate that
the implementation of this new standard will materially impact earnings per
share.
 
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<PAGE>   6
 
                       FRIEDMAN INDUSTRIES, INCORPORATED
 
                    MANAGEMENT'S DISCUSSION AND ANALYSIS OF
                 FINANCIAL CONDITION AND RESULTS OF OPERATIONS
 
 THREE MONTHS ENDED JUNE 30, 1997 COMPARED TO THREE MONTHS ENDED JUNE 30, 1996
 
     During the three months ended June 30, 1997, sales, costs of goods sold and
gross profit increased $9,548,953, $8,936,655 and $612,298, respectively, from
the comparable amounts recorded during the three months ended June 30, 1996. The
increases in sales and costs of goods sold were primarily related to coil and
tubular operations which reflected an overall increase in volume of
approximately 33% during the 1997 quarter. Gross profit declined on coil
products and increased on tubular products, the effect of which produced the
increase in gross profit noted above. Gross profit as a percentage of sales was
9.1% and 8.4% for the 1996 and 1997 quarters, respectively. This decline in
margin rates was primarily related to coil operations which produced increased
sales at the expense of margins. Sales of coil products met with stiff
competition during the 1997 quarter. Market demand for tubular products remained
strong during the 1997 quarter.
 
     General, selling and administrative costs increased $246,763 from the
amount recorded in the 1996 quarter. This increase was primarily related to
expenses associated with volume and/or earnings, to costs related to additional
sales employees and to an increase in bad debt expense.
 
     Interest expense declined $18,635. This decline was primarily related to
the reduction in term debt.
 
     Federal income taxes increased $126,601 from the amount recorded during the
1996 quarter due to the increase in earnings before taxes. Tax rates were the
same for both quarters.
 
FINANCIAL POSITION, LIQUIDITY AND CAPITAL RESOURCES
 
     The Company remained in a strong, liquid position at June 30, 1997. Current
ratios were 2.7 and 3.3 at June 30, 1997 and March 31, 1997, respectively.
Working capital was $23,536,934 at June 30, 1997 and $23,184,448 at March 31,
1997. The Company has a line of credit arrangement with a bank whereby it may
borrow up to $8,000,000. At June 30, 1997, borrowings of $4,000,000 had been
made under this line of credit arrangement which expires April 1, 2000.
 
     In July, 1997, the Company secured financing for certain capital
improvements contemplated at its Hickman, Arkansas facility. This financing was
in the form of an amendment to the Company's then-existing credit facility with
its bank. The new credit facility provides for a $4.7 million advancing
promissory note, which converts to a term loan on December 1, 1998 (the "Note").
The Note, which also refinanced the outstanding indebtedness under the Company's
then-existing credit facility, bears interest at a stated interest rate of LIBOR
plus 1.25% and requires quarterly principal payments of $200,000 plus accrued
interest through March 1, 2003. The Company has converted the Note to a fixed
interest rate of 8% for the life of the Note pursuant to a swap transaction with
its bank.
 
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<PAGE>   7
 
                       FRIEDMAN INDUSTRIES, INCORPORATED
                          QUARTER ENDED JUNE 30, 1997
 
PART II -- OTHER INFORMATION
 
ITEM 1. LEGAL PROCEEDINGS
 
     None
 
ITEM 2. CHANGES IN SECURITIES
 
     a). Not applicable
 
     b). Not applicable
 
ITEM 3. DEFAULTS UPON SENIOR SECURITIES
 
     a). None
 
     b). Not applicable
 
ITEM 4. SUBMISSION OF MATTERS TO A VOTE OF SECURITY HOLDERS
 
     Not applicable
 
ITEM 5. OTHER INFORMATION
 
     None
 
ITEM 6. EXHIBITS AND REPORTS ON FORM 8-K
 
     a). Financial Data Schedule
 
<TABLE>
<C>                      <S>
         10.1            -- ISDA Master Agreement between the Company and Texas
                            Commerce Bank National Association ("TCB") dated July 21,
                            1997.
         10.2            -- Advancing Promissory Note of the Company to TCB dated
                            July 21, 1997 in the amount of $4,700,000.
         10.3            -- Second Amendment to amended and restated letter agreement
                            between the Company and TCB dated July 21, 1997.
         27.1            -- Financial Data Schedule.
</TABLE>
 
     b). None
 
                                        6
<PAGE>   8
 
                                   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.
 
                                            FRIEDMAN INDUSTRIES, INCORPORATED
 
Date August 13, 1997                        By        /s/  BEN HARPER
 
                                            ------------------------------------
                                                  Ben Harper, Senior Vice
                                                     President-Finance
                                                 (Chief Accounting Officer)
 
Date August 13, 1997                        By      /s/  HAROLD FRIEDMAN
 
                                            ------------------------------------
                                              Harold Friedman, Vice Chairman of
                                                         the Board
 
                                        7
<PAGE>   9
 
                     INDEPENDENT ACCOUNTANTS' REVIEW REPORT
 
Board of Directors
Friedman Industries, Incorporated
 
We have reviewed the accompanying condensed consolidated balance sheet of
Friedman Industries, Incorporated, as of June 30, 1997, and the related
consolidated statements of earnings and cash flows for the three-month periods
ended June 30, 1997 and 1996. These financial statements are the responsibility
of the Company's management.
 
We conducted our reviews in accordance with standards established by the
American Institute of Certified Public Accountants. A review of interim
financial information consists principally of applying analytical procedures to
financial data and making inquiries of persons responsible for financial and
accounting matters. It is substantially less in scope than an audit conducted in
accordance with generally accepted auditing standards, which will be performed
for the full year with the objective of expressing an opinion regarding the
financial statements taken as a whole. Accordingly, we do not express such an
opinion.
 
Based on our reviews, we are not aware of any material modifications that should
be made to the accompanying condensed consolidated financial statements referred
to above for them to be in conformity with generally accepted accounting
principles.
 
We have previously audited, in accordance with generally accepted auditing
standards, the consolidated balance sheet of Friedman Industries, Incorporated,
as of March 31, 1997, and the related consolidated statements of earnings,
stockholders' equity and cash flows for the year then ended (not presented
herein) and in our report dated May 30, 1997, we expressed an unqualified
opinion on those consolidated financial statements. In our opinion, the
information set forth in the accompanying condensed consolidated balance sheet
as of March 31, 1997, is fairly stated, in all material respects, in relation to
the consolidated balance sheet from which it has been derived.
 
                                          /s/ Ernst & Young LLP
 
Houston, Texas
August 10, 1997
<PAGE>   10
 
                               INDEX TO EXHIBITS
 
<TABLE>
<CAPTION>
        EXHIBIT
         NUMBER                                  DESCRIPTION
        -------                                  -----------
<C>                      <S>
         10.1            -- ISDA Master Agreement between the Company and Texas
                            Commerce Bank National Association ("TCB") dated July 21,
                            1997.
         10.2            -- Advancing Promissory Note of the Company to TCB dated
                            July 21, 1997 in the amount of $4,700,000.
         10.3            -- Second Amendment to amended and restated letter agreement
                            between the Company and TCB dated July 21, 1997.
         27.1            -- Financial Data Schedule.
</TABLE>