<PAGE>   1
 
================================================================================
 
                       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 SEPTEMBER 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 September 30, 1997, the number of shares outstanding of the issuer's
only class of stock was 6,477,138 shares of Common Stock.
================================================================================
<PAGE>   2
 
                        PART I -- FINANCIAL INFORMATION
 
                       FRIEDMAN INDUSTRIES, INCORPORATED
                    CONSOLIDATED BALANCE SHEETS -- UNAUDITED
 
                                     ASSETS
 
<TABLE>
<CAPTION>
                                                              SEPTEMBER 30,     MARCH 31,
                                                                  1997            1997
                                                              -------------    -----------
<S>                                                           <C>              <C>
CURRENT ASSETS
  Cash and cash equivalents.................................   $     74,073    $   168,245
  Accounts receivable, less allowance for doubtful accounts
     ($7,276 at September 30, 1997 and March 31, 1997,
     respectively)..........................................     13,001,857     11,902,925
  Inventories -- Note B.....................................     20,952,075     21,203,665
  Prepaid expenses and other current assets.................        396,024         82,325
                                                               ------------    -----------
          Total Current Assets..............................     34,424,029     33,357,160
PROPERTY, PLANT AND EQUIPMENT
  Land......................................................        198,021        198,021
  Buildings and improvements................................      2,727,450      2,695,913
  Machinery and equipment...................................     13,096,038     11,724,974
  Less allowance for depreciation...........................    (10,137,153)    (9,909,444)
                                                               ------------    -----------
                                                                  5,884,356      4,709,464
OTHER ASSETS
  Cash value of officers' life insurance....................         74,395         50,567
                                                               ------------    -----------
                                                               $ 40,382,780    $38,117,191
                                                               ============    ===========
 
LIABILITIES AND STOCKHOLDERS' EQUITY
 
CURRENT LIABILITIES
  Trade accounts payable and accrued expenses...............   $  7,804,827    $ 8,112,096
  Current portion of long-term debt.........................        800,000        800,000
  Dividends payable.........................................        485,780        369,715
  Contribution to profit-sharing plan.......................        124,998        242,000
  Federal income taxes payable..............................             --        256,434
  Employee compensation and related expenses................        485,248        392,427
                                                               ------------    -----------
          Total Current Liabilities.........................      9,700,853     10,172,672
LONG-TERM DEBT, less current portion........................      6,100,000      4,600,000
PROVISION FOR NONPENSION RETIREMENT BENEFITS................        113,000        113,000
DEFERRED INCOME TAXES.......................................        419,560        449,560
STOCKHOLDERS' EQUITY
Common stock:
  Par value $1 per share:
     Authorized 10,000,000 shares; Issued and outstanding
       shares -- 6,477,138 at September 30, 1997 and
       6,161,994 at
       March 31, 1997.......................................      6,477,138      6,161,994
  Additional paid-in capital................................     23,653,105     22,377,246
  Retained earnings.........................................     (6,080,876)    (5,757,281)
                                                               ------------    -----------
          Total Stockholders' Equity........................     24,049,367     22,781,959
                                                               ------------    -----------
                                                               $ 40,382,780    $38,117,191
                                                               ============    ===========
</TABLE>
 
                                        1
<PAGE>   3
 
                       FRIEDMAN INDUSTRIES, INCORPORATED
 
                CONSOLIDATED STATEMENT OF EARNINGS -- UNAUDITED
 
<TABLE>
<CAPTION>
                                               THREE MONTHS ENDED           SIX MONTHS ENDED
                                                  SEPTEMBER 30,               SEPTEMBER 30,
                                            -------------------------   -------------------------
                                               1997          1996          1997          1996
                                            -----------   -----------   -----------   -----------
<S>                                         <C>           <C>           <C>           <C>
Net sales.................................  $36,961,370   $29,486,754   $75,261,802   $58,238,233
Costs and expenses
  Costs of goods sold.....................   34,065,469    26,956,145    69,131,090    53,085,111
  General, selling and administrative
     costs................................    1,251,526       978,013     2,605,254     2,084,978
  Interest................................      112,146       129,605       227,734       263,828
                                            -----------   -----------   -----------   -----------
                                             35,429,141    28,063,763    71,964,078    55,433,917
Interest and other income.................      (10,091)      (28,511)      (27,270)      (57,507)
                                            -----------   -----------   -----------   -----------
Earnings before federal income taxes......    1,542,320     1,451,502     3,324,994     2,861,823
Provision (benefit) for federal income
  taxes:
  Current.................................      539,389       506,010     1,160,499       998,019
  Deferred................................      (15,000)      (12,500)      (30,000)      (25,000)
                                            -----------   -----------   -----------   -----------
                                                524,389       493,510     1,130,499       973,019
                                            -----------   -----------   -----------   -----------
Net earnings..............................  $ 1,017,931   $   957,992   $ 2,194,495   $ 1,888,804
                                            ===========   ===========   ===========   ===========
 
Average number of common shares
  outstanding -- Note C...................    6,477,138     6,431,788     6,477,138     6,431,788
                                            ===========   ===========   ===========   ===========
Net earnings per share -- Note C..........        $0.16         $0.15         $0.34         $0.29
                                            ===========   ===========   ===========   ===========
Cash Dividends
  Common Stock -- per share dividend
     declared during periods..............       $0.075         $0.05        $0.145         $0.10
                                            ===========   ===========   ===========   ===========
</TABLE>
 
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<PAGE>   4
 
                       FRIEDMAN INDUSTRIES, INCORPORATED
 
               CONSOLIDATED STATEMENTS OF CASH FLOWS -- UNAUDITED
 
<TABLE>
<CAPTION>
                                                                      SIX MONTHS
                                                                 ENDED SEPTEMBER 30,
                                                              --------------------------
                                                                 1997           1996
                                                              -----------    -----------
<S>                                                           <C>            <C>
OPERATING ACTIVITIES
  Net earnings..............................................  $ 2,194,495    $ 1,888,804
  Adjustments to reconcile net earnings to cash provided by
     operating activities:
     Depreciation...........................................      334,202        316,020
     Provision for deferred taxes...........................      (30,000)       (25,000)
  Decrease (increase) in operating assets:
     Accounts receivable....................................   (1,098,932)       436,328
     Inventories............................................      251,590     (2,959,167)
     Other..................................................     (313,699)      (176,665)
  Increase (decrease) in operating liabilities:
     Accounts payable and accrued expenses..................     (307,269)       981,665
     Contribution to profit-sharing plan....................     (117,002)      (108,000)
     Employee compensation and related expenses.............       92,821        114,749
     Federal income taxes payable...........................     (256,434)        48,019
                                                              -----------    -----------
          NET CASH PROVIDED (USED) BY OPERATING
             ACTIVITIES.....................................      749,772        516,753
INVESTING ACTIVITIES
  Purchase of property, plant and equipment.................   (1,509,095)       (68,461)
  (Increase) decrease in cash value of officers' life
     insurance..............................................      (23,828)       (23,828)
                                                              -----------    -----------
          NET CASH PROVIDED (USED) IN INVESTING
             ACTIVITIES.....................................   (1,532,923)       (92,289)
FINANCING ACTIVITIES
  Cash dividends paid.......................................     (824,871)      (599,575)
  Principal payments on long-term debt......................     (400,000)      (400,000)
  Proceeds from borrowings of long term debt................    1,900,000
  Exercise of stock options.................................       13,850
                                                              -----------    -----------
          NET CASH PROVIDED (USED) IN FINANCING
             ACTIVITIES.....................................      688,979       (999,575)
                                                              -----------    -----------
INCREASE (DECREASE) IN CASH AND CASH EQUIVALENTS............      (94,172)      (575,111)
  Cash and cash equivalents at beginning of period..........      168,245        595,216
                                                              -----------    -----------
CASH AND CASH EQUIVALENTS AT END OF PERIOD..................  $    74,073    $    20,105
                                                              ===========    ===========
</TABLE>
 
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<PAGE>   5
 
                       FRIEDMAN INDUSTRIES, INCORPORATED
 
                     NOTES TO QUARTERLY REPORT -- UNAUDITED
                     THREE MONTHS ENDED SEPTEMBER 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 share are based on the weighted average number of common
shares outstanding. Stock options are not included in the computation of the
weighted average number of common shares outstanding since their effect is not
significant. Fully diluted earnings per share are not presented because they are
not materially dilutive. Applicable per share amounts have been adjusted to give
effect to stock dividends.
 
     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.
 
                                        4
<PAGE>   6
 
                       FRIEDMAN INDUSTRIES, INCORPORATED
 
                    MANAGEMENT'S DISCUSSION AND ANALYSIS OF
                 FINANCIAL CONDITION AND RESULTS OF OPERATIONS
 
 SIX MONTHS ENDED SEPTEMBER 30, 1997 COMPARED TO SIX MONTHS ENDED SEPTEMBER 30,
                                      1996
 
     During the six months ended September 30, 1997, net sales, costs of goods
sold and gross profit increased $17,023,569, $16,045,979 and $977,590,
respectively, from the comparable amounts recorded during the six months ended
September 30, 1996. The increases in net sales and costs of goods sold were
related to coil and tubular operations which reflected a combined increase in
tonnage sold of approximately 29%. Gross profit on coil products declined and
increased on tubular products, the net effect of which resulted in the increase
in gross profit noted above. Gross profit as a percent of sales was 8.8% and
8.1% in the 1996 and 1997 periods, respectively. The decline in margins was
primarily related to coil operations which were adversely affected by stiff
competition within the industry. The Company increased sales of coil products at
the expense of margins. Market conditions for tubular products remained strong
in the 1997 period.
 
     General, selling and administrative costs increased $520,276 from the
amount recorded during the 1996 period. This increase was primarily related to
variable expenses associated with volume and/or earnings, to costs associated
with additional sales employees and to an increase in bad debt expense.
 
     Interest expense and interest and other income declined $36,094 and
$30,237, respectively, from comparable amounts recorded during the 1996 period.
The decline in interest expense was primarily related to a reduction in term
debt. In September 1996, the Company recorded a gain on sale of assets. This
factor combined with reduced average invested cash positions during the 1997
period produced the decline in interest and other income noted above.
 
     Federal income taxes increased $157,480 due to an increase in earnings
before taxes. Effective tax rates were the same for each period.
 
 THREE MONTHS ENDED SEPTEMBER 30, 1997 COMPARED TO THREE MONTHS ENDED SEPTEMBER
                                    30, 1996
 
     During the three months ended September 30, 1997, net sales, costs of goods
sold and gross profit increased $7,474,616, $7,109,324 and $365,292,
respectively, from the comparable amounts recorded during the three months ended
September 30, 1996. The increases in net sales and costs of goods sold were
produced by coil and tubular operations which reflected a combined increase in
tonnage sold of approximately 25%. Gross profit earned on sales of coil products
and on sales of tubular products declined and increased, respectively, the net
effect of which produced the gross profit increase noted above. Gross profit as
a percentage of sales declined from 8.6% in the 1996 quarter to 7.8% in the 1997
quarter. This decline in margin rates was primarily related to coil operations
which were adversely affected by stiff competition within the industry. The
Company increased sales of coil products at the expense of margins. Market
conditions for tubular products remained strong during the 1997 quarter.
 
     General, selling and administrative costs increased $273,513 from the
amount recorded during the 1996 quarter. This increase was primarily related to
an increase in variable expenses associated with volume and/or earnings, to
costs related to additional sales employees, to an increase in bad debt expense
and to other miscellaneous expenses.
 
     Interest expense declined $17,459 primarily as a result of a decline in
term debt.
 
     Interest and other income declined $18,420. This decline was primarily
related to a gain on the sale of assets recorded during the September 1996
quarter.
 
                                        5
<PAGE>   7
 
FINANCIAL POSITION, LIQUIDITY AND CAPITAL RESOURCES
 
     The Company remained in a strong, liquid position at September 30, 1997.
Current ratios were 3.5 and 3.3 at September 30, 1997 and March 31, 1997,
respectively. Working capital was $24,723,176 at September 30, 1997 and
$23,184,448 at March 31, 1997.
 
     The Company has a credit arrangement with a bank pursuant to which the bank
provides a revolving line of credit facility and a term credit facility.
Pursuant to the revolving line of credit facility, the Company may borrow up to
$8 million. The facility expires April 1, 2000. At September 30, 1997, the
Company had borrowings outstanding under the line of credit facility of $5
million. Pursuant to the term credit facility, the Company may borrow up to $4.7
million. Advances made pursuant to the term facility convert to a term loan on
December 1, 1998. The amount outstanding under the term credit facility bear
interest at a stated rate of LIBOR plus 1.25% and requires quarterly principal
payments of $200,000 plus accrued interest, through March 1, 2003. In July 1997,
the Company entered into a swap transaction with the bank pursuant to which it
exchanged the LIBOR-based interest rate obligation for a fixed interest rate
obligation of 8% to remain in effect for the entire term of the term credit
facility. As of September 30, 1997, the principal amount of indebtedness
outstanding under the term credit facility was $1.9 million.
 
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
 
     At the Annual Meeting of Shareholders held on August 22, 1997, the
Company's shareholders elected seven directors to the Company's Board of
Directors. The number of shares voted for and withheld with respect to the
election of each director was as follows:
 
<TABLE>
<CAPTION>
                         NAME                            SHARES VOTED FOR    SHARES WITHHELD
                         ----                            ----------------    ---------------
<S>                                                      <C>                 <C>
Jack Friedman..........................................     6,070,067            28,681
Harold Friedman........................................     6,090,357             8,391
Charles W. Hall........................................     6,040,136            58,612
Alan M. Rauch..........................................     6,040,136            58,612
Hershel M. Rich........................................     6,090,357             8,391
Henry Spira............................................     6,089,256             9,492
Kirk K. Weaver.........................................     6,090,357             8,391
</TABLE>
 
ITEM 5. OTHER INFORMATION
 
     None
 
                                        6
<PAGE>   8
 
ITEM 6. EXHIBITS AND REPORTS ON FORM 8-K
 
     a). 10.1  -- First Amendment to Friedman Industries, Incorporated 1989
                  Incentive Stock Option Plan
 
          10.2  -- First Amendment to Friedman Industries, Incorporated 1995
                   Non-Employee Director Stock Plan
 
          27   -- Financial Data Schedule
 
     b). None
 
                                        7
<PAGE>   9
 
                                   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 November 14, 1997                      By        /s/ BEN HARPER
 
                                             -----------------------------------
                                                   Ben Harper, Senior Vice
                                                       President-Finance
                                                 (Chief Accounting Officer)
 
Date November 14, 1997                      By     /s/ HAROLD FRIEDMAN
 
                                             -----------------------------------
                                              Harold Friedman, Vice Chairman of
                                                           the Board
 
                                        8
<PAGE>   10
                     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 September 30, 1997, the related
consolidated statements of earnings for the three and six month periods ended
September 30, 1997 and 1996 and the consolidated statements of cash flows for 
the six month periods ended September 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
November 14, 1997


                                       9
<PAGE>   11
 
                               INDEX TO EXHIBITS
 
<TABLE>
<CAPTION>
        EXHIBIT
          NO.                                      EXHIBIT
        -------                                    -------
<C>                      <S>                                                          <C>
          10.1           -- First Amendment to Friedman Industries, Incorporated 1989
                            Incentive Stock Option Plan
          10.2           -- First Amendment to Friedman Industries, Incorporated 1995
                            Non-Employee Director Stock Plan
          27             -- Financial Data Schedule
</TABLE>