<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 SEPTEMBER 30, 1996

                         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

 
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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, 1996, the number of shares outstanding of the issuer's
only class of stock was 6,125,512 shares of Common Stock.

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<PAGE>   2
 
                        PART I -- FINANCIAL INFORMATION
 
                       FRIEDMAN INDUSTRIES, INCORPORATED
                    CONSOLIDATED BALANCE SHEETS -- UNAUDITED
 
                                     ASSETS
 
<TABLE>
<CAPTION>
                                                                    SEPTEMBER 30,    MARCH 31,
                                                                        1996           1996
                                                                    ------------    -----------
<S>                                                                 <C>             <C>
CURRENT ASSETS
  Cash and cash equivalents.......................................       $20,105    $   595,216
  Accounts receivable, less allowance for doubtful accounts
     ($5,794 at September 30, 1996 and March 31, 1996,
     respectively)................................................     8,986,876      9,423,204
  Inventories -- Note B...........................................    20,350,792     17,391,625
  Prepaid expenses and other current assets.......................       291,290        114,625
                                                                    ------------    -----------
          Total Current Assets....................................    29,649,063     27,524,670
PROPERTY, PLANT AND EQUIPMENT
  Land............................................................       198,021        198,021
  Buildings and improvements......................................     2,695,912      2,687,730
  Machinery and equipment.........................................    11,706,794     11,699,234
  Less allowance for depreciation.................................   (9,579,873)     (9,316,572)
                                                                    ------------    -----------
                                                                       5,020,854      5,268,413
OTHER ASSETS
  Cash value of officers' life insurance..........................        43,731         19,903
                                                                    ------------    -----------
                                                                     $34,713,648    $32,812,986
                                                                      ==========     ==========
                          LIABILITIES AND STOCKHOLDERS' EQUITY
CURRENT LIABILITIES
  Trade accounts payable and accrued expenses.....................    $5,720,874    $ 4,739,206
  Current portion of long-term debt...............................       800,000        800,000
  Dividends payable...............................................       306,959        291,709
  Contribution to profit-sharing plan.............................       108,000        216,000
  Federal income taxes payable....................................       101,066         53,047
  Employee compensation and related expenses......................       425,314        310,565
                                                                    ------------    -----------
          Total Current Liabilities...............................     7,462,213      6,410,527
LONG-TERM DEBT, less current portion..............................     5,000,000      5,400,000
PROVISION FOR NONPENSION RETIREMENT BENEFITS......................       113,000        113,000
DEFERRED INCOME TAXES.............................................       435,523        460,523
STOCKHOLDERS' EQUITY
Common stock:
  Par value $1 per share:
     Authorized 10,000,000 shares; Issued and outstanding
      shares -- 6,125,512 at September 30, 1996 and 5,834,195 at
      March 31, 1996..............................................     6,125,512      5,834,195
  Additional paid-in capital......................................    22,336,517     21,444,360
  Retained earnings...............................................   (6,759,117)     (6,849,619)
                                                                    ------------    -----------
          Total Stockholders' Equity..............................    21,702,912     20,428,936
                                                                    ------------    -----------
                                                                     $34,713,648    $32,812,986
                                                                      ==========     ==========
</TABLE>
 
                                        1
<PAGE>   3
 
                       FRIEDMAN INDUSTRIES, INCORPORATED
 
                CONSOLIDATED STATEMENT OF EARNINGS -- UNAUDITED
 
<TABLE>
<CAPTION>
                                                THREE MONTHS ENDED            SIX MONTHS ENDED 
                                                  SEPTEMBER 30,                 SEPTEMBER 30,
                                            --------------------------    --------------------------
                                               1996           1995           1996           1995
                                            -----------    -----------    -----------    -----------
<S>                                         <C>            <C>            <C>            <C>
Net sales.................................  $29,486,754    $26,208,387    $58,238,233    $54,961,052
Costs and expenses
  Costs of goods sold.....................   26,956,145     24,433,119     53,085,111     50,919,317
  General, selling and administrative
     costs................................      978,013        789,582      2,084,978      1,713,371
  Interest................................      129,605        167,557        263,828        334,249
                                            -----------    -----------    -----------    -----------
                                             28,063,763     25,390,258     55,433,917     52,966,937
Interest and other income.................      (28,511)       (21,291)       (57,507)       (31,994)
                                            -----------    -----------    -----------    -----------
Earnings before federal income taxes......    1,451,502        839,420      2,861,823      2,026,109
Provision (benefit) for federal income
  taxes:
  Current.................................      506,010        297,902        998,019        713,877
  Deferred................................      (12,500)       (12,500)       (25,000)       (25,000)
                                            -----------    -----------    -----------    -----------
                                                493,510        285,402        973,019        688,877
                                            -----------    -----------    -----------    -----------
Net earnings..............................  $   957,992    $   554,018    $ 1,888,804    $ 1,337,232
                                             ==========     ==========     ==========     ==========
Net earnings per share -- Note D..........        $0.16          $0.09          $0.31          $0.22
                                             ==========     ==========     ==========     ==========
Cash Dividends
  Common Stock -- per share dividend
     declared during periods (shares
     outstanding at record date:
6,125,512 in 1996 and 5,832,195 in 1995)..        $0.05          $0.05          $0.10          $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,
                                                                    ---------------------------
                                                                       1996            1995
                                                                    -----------     -----------
<S>                                                                 <C>             <C>
OPERATING ACTIVITIES
  Net earnings....................................................  $ 1,888,804     $ 1,337,232
  Adjustments to reconcile net earnings to cash provided by
     operating activities:
     Depreciation.................................................      316,020         297,526
     Provision for deferred taxes.................................      (25,000)        (25,000)
  Decrease (increase) in operating assets:
     Accounts receivable..........................................      436,328         290,365
     Inventories..................................................   (2,959,167)     (1,327,828)
     Other........................................................     (176,665)       (180,400)
  Increase (decrease) in operating liabilities:
     Accounts payable and accrued expenses........................      981,665         950,688
     Contribution to profit-sharing plan..........................     (108,000)       (100,000)
     Employee compensation and related expenses...................      114,749          13,941
     Federal income taxes payable.................................       48,019         (14,658)
                                                                    -----------     -----------
          NET CASH PROVIDED (USED) BY OPERATING ACTIVITIES........      516,753       1,241,866
INVESTING ACTIVITIES
  Purchase of property, plant and equipment.......................      (68,461)       (398,791)
  (Increase) decrease in cash value of officers' life
     insurance -- Note C..........................................      (23,828)        689,320
                                                                    -----------     -----------
          NET CASH PROVIDED (USED) IN INVESTING ACTIVITIES........      (92,289)        290,529
FINANCING ACTIVITIES
  Cash dividends paid.............................................     (599,575)       (571,025)
  Principal payments on long-term debt............................     (400,000)     (2,200,000)
  Proceeds from borrowings of long term debt......................                    1,000,000
                                                                    -----------     -----------
          NET CASH PROVIDED (USED) IN FINANCING ACTIVITIES........     (999,575)     (1,771,025)
                                                                    -----------     -----------
INCREASE (DECREASE) IN CASH AND CASH EQUIVALENTS..................     (575,111)       (238,630)
  Cash and cash equivalents at beginning of period................      595,216         664,527
                                                                    -----------     -----------
CASH AND CASH EQUIVALENTS AT END OF PERIOD........................  $    20,105     $   425,897
                                                                     ==========      ==========
</TABLE>
 
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<PAGE>   5
 
                       FRIEDMAN INDUSTRIES, INCORPORATED
 
                     NOTES TO QUARTERLY REPORT -- UNAUDITED
                     THREE MONTHS ENDED SEPTEMBER 30, 1996
 
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, 1996.
 
NOTE B -- INVENTORIES
 
     Coil inventory consists primarily of raw materials. Tubular inventory is
comprised of both raw materials and finished goods.
 
NOTE C -- CASH VALUE OF OFFICERS' LIFE INSURANCE
 
     In July 1995, the Company borrowed $708,168 against the cash surrender
value of officers' life insurance policies (the "borrowings"). The borrowings do
not require specific repayment terms except that in case of a death, the
borrowings will be deducted from the proceeds of the life insurance policy. The
proceeds of the borrowings were used to reduce the term note.
 
NOTE D -- EARNINGS PER SHARE
 
     Earnings per common and common equivalent share for the periods ended
September 30, 1996 and September 30, 1995 are based on the weighted average
number of common and common equivalent (stock options) shares outstanding as
follows:
 
<TABLE>
<CAPTION>
                                                                      1996          1995
                                                                    ---------     ---------
    <S>                                                             <C>           <C>
    Common Stock:
      Shares outstanding during the entire period.................  5,834,195     5,554,858
      Retroactive effect of stock dividends declared..............    291,317       568,947
                                                                    ---------     ---------
              Weighted average number of common and common
                equivalent shares.................................  6,125,512     6,123,805
                                                                    =========     =========
</TABLE>
 
     Earnings per share assuming full dilution for the quarters ended September
30, 1996 and 1995, 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.
 
                                        4
<PAGE>   6
 
                       FRIEDMAN INDUSTRIES, INCORPORATED
 
                    MANAGEMENT'S DISCUSSION AND ANALYSIS OF
                 FINANCIAL CONDITION AND RESULTS OF OPERATIONS
 
          SIX MONTHS ENDED SEPTEMBER 30, 1996 COMPARED TO SIX MONTHS
                           ENDED SEPTEMBER 30, 1995
 
     During the six months ended September 30, 1996, net sales, costs of goods
sold and gross profit increased $3,277,181, $2,165,794 and $1,111,387,
respectively, from the comparable amounts recorded during the six months ended
September 30, 1995. The increase in sales was primarily related to volume
increases associated with coil and tubular operations. Both operations benefited
from improved market conditions during the 1996 period. The increase in costs of
goods sold primarily resulted from the increase in sales noted above. The
increase in gross profit was principally related to improved margins and
increased sales. Margin rates were 8.85% and 7.35% in the 1996 and 1995 periods,
respectively. Management believes that stronger demand for the Company's
products was the primary factor associated with the increase in margins.
 
     General, selling and administrative costs increased $371,607 from the
amount recorded during the 1995 period. This increase was primarily related to
increases in expenses associated with volume and/or earnings such as employee
incentive bonuses and commissions, franchise taxes, contribution to profit
sharing plan and other variable expenses. In addition, increases in rental costs
and officer compensation relative to executive promotions contributed to the
overall increase.
 
     Interest expense declined $70,421 from the amount recorded during the 1995
period. This decrease primarily resulted from a reduction in term debt and lower
interest rates on a period-to-period basis.
 
     Interest and other income increased $25,513. This increase was primarily
related to a gain on the sale of machinery and equipment.
 
     Federal income taxes increased $284,142 as a result of the increase in
earnings before federal income taxes. Tax rates were the same during each
period.
 
        THREE MONTHS ENDED SEPTEMBER 30, 1996 COMPARED TO THREE MONTHS
                           ENDED SEPTEMBER 30, 1995
 
     During the three months ended September 30, 1996, net sales, costs of goods
sold and gross profit increased $3,278,367, $2,523,026 and $755,341 from the
respective amounts recorded during the three months ended September 30, 1995.
The sales and costs of goods sold increases were primarily related to volume
increases associated with coil and tubular operations. The gross profit increase
was principally related to improved margins (8.58% in the 1996 quarter and 6.77%
in the 1995 quarter) and the above noted sales increase. Demand for coil and
tubular products was stronger in the 1996 quarter when compared to the 1995
quarter and supported improved sales and margins.
 
     General, selling and administrative costs increased $188,431 from the
comparable amount recorded in the 1995 quarter. This increase was primarily
related to variable expenses associated with volume and/or earnings.
Additionally, officer compensation relative to executive promotions increased
during the 1996 quarter.
 
     Interest expense declined $37,952 from the amount recorded in the 1995
quarter. This decrease was principally related to a reduction in term debt and
lower interest rates paid on borrowed funds in the 1996 quarter.
 
     Federal income taxes increased $208,108 as a result of the increase in
earnings before federal income taxes. Effective tax rates were the same for each
quarter.
 
FINANCIAL POSITION, LIQUIDITY AND CAPITAL RESOURCES
 
     The Company remained in a strong, liquid position at September 30, 1996.
Current ratios were 4.0 and 4.3 at September 30, 1996, and March 31, 1996,
respectively. Working capital was $22,186,850 at September 30, 1996, and
$21,114,143 at March 31, 1996. The Company has a line of credit arrangement with
 
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<PAGE>   7
 
a bank whereby it may borrow up to $8,000,000. At September 30, 1996, borrowings
of $4,000,000 had been made under this line of credit arrangement which expires
April 1, 1998.
 
     In July 1995, the Company borrowed $708,168 against the cash surrender
value of officers' life insurance policies and used such proceeds to reduce
outstanding indebtedness under the Company's term note. See also Note C
appearing herein.
 
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 30, 1996, the
Company's shareholders elected seven directors to the Company's Board of
Directors and approved the Friedman Industries, Incorporated 1996 Employee Stock
Option Plan. 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..........................................     5,235,463             35,350
    Harold Friedman........................................     5,235,770             35,043
    Charles W. Hall........................................     4,994,793            276,020
    Alan M. Rauch..........................................     5,235,770             35,043
    Hershel M. Rich........................................     5,232,050             38,763
    Henry Spira............................................     5,231,510             39,303
    Kirk K. Weaver.........................................     5,235,770             35,043
</TABLE>
 
     The number of shares voted for, against and abstain with respect to the
1996 Employee Stock Option Plan was as follows:
 
<TABLE>
                    <S>                                         <C>
                    For.......................................  5,204,733
                                                                ---------
                    Against...................................     78,431
                                                                ---------
                    Abstain...................................     21,525
                                                                ---------
</TABLE>
 
ITEM 5. OTHER INFORMATION
 
     None
 
ITEM 6. EXHIBITS AND REPORTS ON FORM 8-K
 
     a). Financial Data Schedule
 
     b). None
 
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<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 November 13, 1996                      By        /s/  BEN HARPER
                                            ------------------------------------
                                                  Ben Harper, Senior Vice
                                                     President-Finance
                                                 (Chief Accounting Officer)
 
Date November 13, 1996                      By      /s/  HAROLD FRIEDMAN
                                            ------------------------------------
                                              Harold Friedman, Vice Chairman of
                                                         the Board
 
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<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 September 30, 1996, the related
consolidated statements of earnings for the three-month and six-month periods
ended September 30, 1996 and 1995 and the consolidated statements of cash flows
for the six-month periods ended September 30, 1996 and 1995. 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, 1996 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 28, 1996, 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, 1996 is fairly stated, in all material respects, in relation to
the consolidated balance sheet from which it has been derived.
 
                                          ERNST & YOUNG LLP
 
November 9, 1996
<PAGE>   10
                            INDEX TO EXHIBITS


          Exhibit
            No.                      Description
          -------                    ----------- 
            27                 Financial Data Schedule