<PAGE>   1
                                                                    EXHIBIT 10.1


            THIRD AMENDMENT TO AMENDED AND RESTATED LETTER AGREEMENT
                             (WITH BORROWING BASE)

THIS THIRD AMENDMENT TO AMENDED AND RESTATED LETTER AGREEMENT (this
"Amendment") dated effective as of April 1, 1999 (the "Effective Date"), is by
and between FRIEDMAN INDUSTRIES, INCORPORATED ("Borrower"), and CHASE BANK OF
TEXAS, NATIONAL ASSOCIATION, formerly known as TEXAS COMMERCE BANK NATIONAL
ASSOCIATION, a national banking association ("Bank").

PRELIMINARY STATEMENT. Bank and Borrower have entered into an Amended And
Restated Letter Agreement dated as of April 1, 1995, as amended by a First
Amendment to Amended and Restated Letter Agreement dated as of April 1, 1997,
and a Second Amendment to Amended and Restated Letter Agreement dated as of
July 21, 1997 (collectively, "Credit Agreement"). The "Agreement", as used in
the Credit Agreement, shall also refer to the Credit Agreement as amended by
this Amendment. All capitalized terms defined in the Credit Agreement and not
otherwise defined herein shall have the same meanings herein as in the Credit
Agreement. Bank and Borrower have agreed to amend the Credit Agreement to the
extent set forth herein, and in order to, among other things, renew, modify and
extend the Revolving Credit Note.

NOW THEREFORE, in consideration of the premises and other good and valuable
consideration, the receipt and sufficiency of which are hereby acknowledged by
the parties hereto, Bank and Borrower hereby agree as follows:

1. Revolving Credit Note. Section 1.1 of the Credit Agreement is amended by
substituting the following for the Section 1.1 of the Credit Agreement:

         "Subject to the terms and conditions hereof, the Bank agrees to make
         loans ("Loan" or "Loans") to Borrower from time to time before the
         Termination Date, as defined in the Credit Agreement between Bank and
         Borrower, not to exceed at any one time outstanding $8,000,000.00 (the
         "Commitment"), Borrower having the right to borrow, repay and reborrow.
         Bank and Borrower agree that Chapter 346 of the Texas Finance Code
         shall not apply to this Agreement, the Note or any Loan. The Loans
         shall be evidenced by and shall bear interest and be payable as
         provided in the promissory note of Borrower dated the Effective Date
         (together with any and all renewals, extensions, modifications,
         replacements, and rearrangements thereof and substitutions therefor,
         the "Note"), which is given in renewal, modification and extension of
         that certain promissory note dated April 1, 1997, maturing April 1,
         2000, in the original principal amount of $8,000.000.00 (including all
         prior notes of which said note represents a renewal, extension,
         modification, increase, substitution, rearrangement or replacement
         thereof, the "Renewed Note"). The parties hereto agree that there is
         as of the Effective Date an outstanding principal balance of
         $4,000,000.00 under the Note leaving a balance as of the Effective
         Date of $4,000,000.00 under the Commitment available for Loans subject
         to the terms and conditions of this Agreement. The "Note" as used in
         the Credit Agreement shall also refer to the "Note" as used in this
         Amendment. The purpose of the Loans is: business (working capital
         support)."

2. Termination Date is hereby defined as the earlier of: (a) April 1, 2002; or
(b) the date on which the maturity of the Notes is accelerated in accordance
with Section 5 of the Credit Agreement.

3. Section 2.1 (c) of the Credit Agreement is amended to read "December
31, 1998" for the date of the last financial statement delivered to the Bank.

4. Section 4.2 of the Credit Agreement is amended to read as follows:

         "SECTION 4.2 FINANCIAL COVENANTS Comply with each of the affirmative
         covenants set forth in Exhibit A and furnish to Bank: (i) the financial
         statements prepared in conformity with GAAP on consolidated and
         consolidating bases and the other information described in, and within
         the times required by, Exhibit A Reporting Requirements, Financial
         Covenants and Compliance Certificate attached hereto and incorporated
         herein by reference; and (ii) within the time required by Exhibit A,
         Exhibit A signed and certified by the chief financial officer or
         president of Borrower."

5. Exhibit A of the Credit Agreement is amended by replacing existing Exhibit A
with the Exhibit A attached hereto for all purposes, which shall be a quarterly
compliance certificate as further described therein.

6. Borrower hereby represents and warrants to the Bank that after giving effect
to the execution and delivery of this Amendment: (a) the representations and
warranties set forth in the Credit Agreement are true and correct an the date
hereof as though made on and as of such date; and (b) no Event of Default, or
event which with passage of time, the giving of notice or both would become an
Event of Default, has occurred and is continuing as of the date hereof.

7. This Amendment shall become effective as of the Effective Date upon its
execution and delivery by each of the parties named in the signature lines
below, and the "Agreement" as used in the Credit Agreement shall also refer to
the Credit Agreement as amended by this Amendment.

8. Borrower further acknowledges that each of the other Loan Documents is in
all other respects ratified and confirmed, and all of the rights, powers and
privileges created thereby or thereunder are, ratified, extended, carried
forward and remain in full force and effect except as the Credit Agreement is
amended by this Amendment.

9. This Amendment may be executed in any number of counterparts and by
different parties hereto in separate counterparts, each of which when so
executed shall be deemed an original and all of which taken together shall
constitute but one and the same agreement.

10. This Amendment shall be included within the definition of "Loan Documents"
as used in the Agreement.

11. THIS AMENDMENT SHALL BE GOVERNED BY AND CONSTRUED IN ACCORDANCE WITH THE
LAWS OF THE STATE OF TEXAS AND AS APPLICABLE, THE LAWS OF THE UNITED STATES OF
AMERICA.

THIS WRITTEN AMENDMENT AND THE OTHER LOAN DOCUMENTS CONSTITUTE A "LOAN
AGREEMENT" AS DEFINED IN SECTION 26.02(a) OF THE TEXAS BUSINESS & COMMERCE
CODE, AND REPRESENTS THE FINAL AGREEMENT BETWEEN THE PARTIES AND MAY NOT BE
CONTRADICTED BY EVIDENCE OF PRIOR, CONTEMPORANEOUS OR SUBSEQUENT ORAL
AGREEMENTS OF THE PARTIES. THERE ARE NO UNWRITTEN ORAL AGREEMENTS BETWEEN THE
PARTIES.




                               Page 1 of 2 Pages


<PAGE>   2





IN WITNESS WHEREOF, the parties hereto have caused this Amendment [ILLEGIBLE]
Date.

                   BORROWER:  FRIEDMAN INDUSTRIES INCORPORATED

                              By: /s/ BEN HARPER
                                 ----------------------------------------
                              Name: Ben Harper
                                   --------------------------------------
                              Title: Senior Vice President - Finance
                                    -------------------------------------
                              Address:  P.O. Box 21147, Houston, TX 77226
                                      -----------------------------------

                   BANK:      CHASE BANK OF TEXAS, NATIONAL ASSOCIATION

                              By: /s/ KEVIN K. RECH
                                 ----------------------------------------
                              Name: Kevin K. Rech
                                   --------------------------------------
                              Title: Vice President
                                    -------------------------------------
                              Address:  545 W 19th Houston, TX 77008
                                      -----------------------------------




                               Page 2 of 2 Pages



<PAGE>   3



                         EXHIBIT A TO AGREEMENT BETWEEN
    FRIEDMAN INDUSTRIES, INCORPORATED ("BORROWER") AND CHASE BANK OF TEXAS,
                         NATIONAL ASSOCIATION ("BANK")
               DATED AS OF APRIL 1, 1995, AS SAME MAY BE AMENDED,
                      RESTATED AND SUPPLEMENTED IN WRITING

                  REPORTING REQUIREMENTS, FINANCIAL COVENANTS
                                      AND
 COMPLIANCE CERTIFICATE FOR CURRENT REPORTING PERIOD ENDING ____________, 199_
                                  ("END DATE")

A. REPORTING PERIOD. THIS EXHIBIT WILL BE IN PROPER FORM AND BE SUBMITTED
   QUARTERLY.

<TABLE>
<S>                               <C>                                                                                   <C>
B.
===================================================================================================================================
 Financial Reporting. Borrower will provide the following financial information
                      within the times indicated:                                                                       Compliance
                                                                                                                        Certificate
===================================================================================================================================
          WHO                     WHEN DUE                   WHAT                                                       Compliance
                                                                                                                         (Circle)
                                                                                                                          Yes   No
-----------------------------------------------------------------------------------------------------------------------------------
BORROWER               (i) Quarterly at such time as this statement is     Borrower's 10-Q together with a                Yes   No
                       submitted to the Securities and Exchange            certificate of compliance duly executed by
                       Commission ("SEC")                                  an officer of Borrower
                       ------------------------------------------------------------------------------------------------------------
                       (ii) On an annual basis at such time as this        Borrower's 10-K together with a                 Yes  No
                       statement is submitted to the Securities and        certificate of compliance duly executed by
                       Exchange Commission ("SEC")                         an officer of Borrower
===================================================================================================================================

C.
===================================================================================================================================
FINANCIAL COVENANTS. Borrower will comply with the                              COMPLIANCE CERTIFICATE
following financial covenants, defined in accordance with GAAP
incorporating the calculation adjustments indicated on the Compliance
Certificate:
-----------------------------------------------------------------------------------------------------------------------------------
                 REQUIRED                                                                 ACTUAL REPORTED              Compliance
                                                                                                                        (Circle)
Except as specified otherwise, each covenant will be maintained at all     For Current Reporting Period/as               Yes    No
times and reported for each Reporting Period or as of each Reporting       of the End Date
Period End Date, as appropriate:
-----------------------------------------------------------------------------------------------------------------------------------
1. Maintain a Working Capital of at least $10,000,000.00.                  $____________ - $______________ = $__________ Yes    No
                                                                             Current Assets Current Liabilities Working Capital
-----------------------------------------------------------------------------------------------------------------------------------
2. Maintain a Tangible Net Worth as adjusted of at least                        Stockholders' Equity        $ __________  Yes   No
   $22,500,000.00 at all times.                                                 Minus:   Goodwill           $ __________

                                                                                         Other Intangible
     Thereafter, said required minimum Tangible Net Worth to be increased                Assets             $ __________
     annually calculated as the amount equal to the sum of (x) the              Plus:    Subordinated Debt  $ __________
     immediately preceding year's required amount plus (y) 20% of the
     immediately preceding year's net income.                                   Equals Tangible Net Worth   $ __________

                                                                               Beginning April 1, 1999 and until March 31, 2000:
                                                                                       $22,500,000.00

                                                                               Beginning April 1, 2000 and until March 31, 2001:
                                                                                     (x) $22,500,000.00
                                                                                Plus (y) $_____________
                                                                               Equals: Required minimum Tangible Net Worth $ _____

                                                                                Beginning April 1, 2001 and thereafter:
                                                                                     (x) $____________
                                                                                Plus (y) $____________
                                                                                Equals: Required minimum Tangible Net Worth $_____


-----------------------------------------------------------------------------------------------------------------------------------
    3. Maintain a Current Ratio of at least 2.00 to 1.00.                $____________  / $______________=$__________  Yes   No
                                                                        Current Assets Current Liabilities Current Ratio
-----------------------------------------------------------------------------------------------------------------------------------
    4. Maintain a ratio of Total Indebtedness to Tangible Net Worth plus        Total Indebtedness (GAAP)  $_________   Yes   No
       Subordinated Debt no greater than 1.10 to 1.00 at all times

                                                                                  Tangible Net Worth $ ___________
                                                                                $ ______________ / $ ____________ = $ _____________
                                                                              Total Indebtedness    Tangible Net Worth      Ratio
===================================================================================================================================
</TABLE>



                          EXHIBIT A Page 1 of 2 Pages


<PAGE>   4


<TABLE>



===================================================================================================================================
<S>                                                   <C>                                                       <C>
5. Maintain a fixed charge ratio all times for the    For all items except maturities of long term debt,           YES    NO
   preceding 12 month period as of March 31, of       show amounts for current month plus previous 11 months:
   each year of at least 1.25 to 1.00.

                                                      Ordinary Net income                       $__________
                                                      Plus:     Depreciation                    $__________
                                                                Interest Expense                $__________
                                                                Tax Expense                     $__________
                                                      Minus:    Cash taxes                      $__________
                                                      Equals:   Available Cash Flow             $__________

                                                      Scheduled Principal
                                                      Payments made by Borrower                 $__________

                                                      Plus:     Interest Expense                $__________
                                                                Capital Expenditures
                                                                (non-financed)                  $__________

                                                      Equals:   Total Fixed Charges             $__________

                                                     $___________________/    $__________________  = ______
                                                      Available Cash Flow      Total Fixed Charges   Ratio


===================================================================================================================================
</TABLE>


THE ABOVE SUMMARY REPRESENTS SOME OF THE COVENANTS AND AGREEMENTS CONTAINED IN
THE NOTE AND DOES NOT IN ANY WAY RESTRICT OR MODIFY THE TERMS AND CONDITIONS OF
THE NOTE. IN CASE OF CONFLICT BETWEEN THIS EXHIBIT A AND THE NOTE, THE NOTE
SHALL CONTROL.

The undersigned hereby certifies that the above information and computations
are true and correct and not misleading as of the date hereof, and that since
the date of the Borrower's most recent Compliance Certificate (if any):

   [ ]      No default or Event of Default has occurred under the Note during
            the current Reporting Period, or been discovered from a prior
            period, and not reported.

   [ ]      A default or Event of Default (as described below) has occurred
            during the current Reporting Period or has been discovered from a
            prior period and is being reported for the first time and:

            [ ]       was cured on _______________.

            [ ]       was waived by Bank in writing on _______________.

            [ ]       is continuing.

   Description of Event of Default:
                                   --------------------------------------------

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


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



Executed this                   day of                 , 19
              ----------------        ----------------

BORROWER: FRIEDMAN INDUSTRIES, INCORPORATED

SIGNATURE:
          ---------------------------------------------------------------------
NAME:
     --------------------------------------------------------------------------
TITLE:
      -------------------------------------------------------------------------
ADDRESS:
        -----------------------------------------------------------------------

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                          EXHIBIT A Page 2 of 2 Pages