<PAGE>   1
                                                                   EXHIBIT 10.2


                                 FIRST AMENDMENT
                                       TO
                                CREDIT AGREEMENT


THIS FIRST AMENDMENT TO CREDIT AGREEMENT, dated as of this 27th day of December,
2000 (this "First Amendment"), by and among UNITED STATES LIME & MINERALS, INC.,
a Texas corporation ("U.S. Lime"), TEXAS LIME COMPANY, a Texas corporation
wholly owned by U.S. Lime ("TLC"), ARKANSAS LIME COMPANY, an Arkansas
corporation wholly owned by U.S. Lime ("ALC") (U.S. Lime, TLC and ALC are
collectively referred to as "Borrowers" and individually as a "Borrower"), the
Lenders who are a party to that certain Credit Agreement dated as of April 22,
1999 by and among the Borrowers, such Lenders (collectively, the "Lenders"), and
FIRST UNION NATIONAL BANK, as Administrative Agent for such Lenders
(respectively, the "Credit Agreement" and the "Administrative Agent").

                                    BACKGROUND

         A. Borrowers, Lenders, and Administrative Agent for itself and the
other Lenders are parties to the Credit Agreement, pursuant to which the Lenders
have agreed, subject to the terms and conditions of the Credit Agreement, to
lend to Borrowers the sum of Fifty Million Dollars ($50,000,000) on a term loan
basis secured by substantially all of the respective Borrowers' personal
property other than Accounts, Inventory, and related personal property, and by
mortgages or deeds of trust on certain real property owned by ALC and TLC. All
initially capitalized terms used herein and not otherwise defined herein shall
have the same meaning as ascribed to such terms in the Credit Agreement.

         B. Pursuant to Section 12.11 of the Credit Agreement, Borrower has
sought the consent of the Lenders to borrow Five Million Dollars ($5,000,000) on
an unsecured fully subordinated basis and to amend certain covenants as set
forth in the Credit Agreement, which covenants would be affected by the creation
of such additional Debt, and no less than the Required Lenders have agreed to
grant their consent to the incurrence of such additional indebtedness and
amendment to such covenants, subject to the terms, conditions and provisions
hereof.

         NOW, THEREFORE, in consideration of the foregoing and of the mutual
covenants set forth herein, the parties hereto, intending to be legally bound
hereby, agree as follows:

         1. Ratification. This First Amendment is a modification of the Credit
Agreement pursuant to Section 12.11 thereof. Except as expressly set forth
herein, or in any amendment to any of the documents referred to herein,
Borrowers, the Required Lenders and the Administrative Agent acknowledge and
agree that each and every term, condition and provision of the Loan Agreement is
hereby ratified and confirmed in full.


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         2. Outstanding Indebtedness. Borrowers hereby unconditionally
acknowledge that, as of the date hereof, the principal balance due and owing to
the Lenders under the Credit Agreement is Forty-Seven Million Seven Hundred
Seventy-Seven Thousand Dollars and Sixty-Eight Cents ($47,777,777.68), and that
such amount, together with interest thereon at the rates set forth therein, is
owing to the Lenders without claim, counterclaim, recoupment, defense or setoff
of any kind.

         3. The Subordinated Debt. Provided that no Event of Default has
occurred under the Credit Agreement as amended by this First Amendment and all
of the conditions precedent as hereinafter set forth have been fulfilled to the
satisfaction of the Administrative Agent, the Lenders which are parties to this
First Amendment consent to the incurrence by the Borrowers of the indebtedness
evidenced by that certain subordinated promissory note of the Borrowers of even
date herewith in favor of INBERDON ENTERPRISES LTD., in the form thereof
attached hereto as Exhibit "A" (the "Subordinated Note") and to the repayment
thereof in accordance with paragraph (h) of the Subordination Provisions
contained therein. It is intended that subject to the consent of the Required
Lenders the indebtedness to be evidenced by the Subordinated Note shall
constitute Subordinated Debt under the Credit Agreement, as amended by this
First Amendment. For the purposes of applying the covenant set forth in Section
9.1(h) only, the Indebtedness under the Subordinated Debt shall not be included
in the definition of Debt.

         4. Indebtedness Under the Working Capital Facility. Section 9.1(d) is
hereby amended and restated in its entirety as follows:

            (d) Indebtedness outstanding under the Working Capital Facility;

         5. Representations and Warranties. To induce the Required Lenders to
enter into this First Amendment, Borrowers jointly and severally represent and
warrant to the Lenders and Administrative Agent as follows:

               5.1 After giving effect to the modifications contained herein,
all representations, warranties and covenants made by Borrowers to the Lenders
and the Administrative Agent in the Credit Agreement (except those relating to a
specific date) are true and correct in all material respects as of the date
hereof, with the same force and effect as though made as of the date hereof;

               5.2 No Event of Default or Default has occurred and is continuing
under the Loan Agreement as of the date hereof;

               5.3 Each Borrower is a corporation validly subsisting under the
laws of the state of its incorporation; the execution, delivery and performance
of this First Amendment and any other



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documents and instruments executed and delivered by the Borrowers to the Lenders
or the Administrative Agent in connection herewith (i) are within each
Borrower's corporate powers, (ii) have been duly authorized by each Borrower's
Board of Directors, (iii) do not contravene any provision of law or any
indenture, agreement or undertaking to which any Borrower is a party or is
otherwise bound, any Borrower's Certificate of Incorporation or bylaws, or any
resolution of the Board of Directors of any Borrower, and (iv) require no
consent or approval of any governmental authority or any third party; and

               5.4 In the case of each Borrower, this First Amendment and any
other documents and instruments executed and delivered by such Borrower to the
Lenders or the Administrative Agent in connection herewith have each been
validly executed by, and are enforceable against, such Borrower in accordance
with their respective terms.

Any failure of any of the representations and warranties made by Borrowers in
this First Amendment to be true and correct in all material respects when made
shall constitute an Event of Default under the Credit Agreement.

         6. Conditions Precedent. The effectiveness of amendments to the Credit
Agreement and the consents set forth herein are subject to the conditions
precedent that the Administrative Agent shall have received ratably for the
benefit of the Lenders, in form and substance satisfactory to the Administrative
Agent:

               6.1 Resolutions of the Board of Directors of each Borrower
authorizing the execution, delivery and performance of this First Amendment, and
the other documents and instruments executed and delivered to the Administrative
Agent in connection herewith, certified by such Borrower's Secretary that the
same are true and complete copies of the originals thereof and remain in full
force and effect, not having been modified or rescinded;

               6.2 The Borrower shall have paid to the Administrative Agent,
ratably for the benefit of the Lenders, an Amendment Fee in the amount of
Thirty-Seven Thousand Five Hundred Dollars ($37,500), which Amendment Fee shall
be deemed fully earned and non-refundable and shall be in addition to, and not
in lieu of, any other fees due and payable under the Credit Agreement or any of
the other Loan Documents; and

               6.3 No less than the Required Lenders shall have executed and
delivered this First Amendment.

         7. Miscellaneous.

               7.1 Entire Agreement. The Loan Agreement, as amended by this
First Amendment, and the other Loan Documents embody the entire agreement and
understanding among the Lenders, the Administrative Agent and Borrowers. The
Loan Agreement, together with




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this First Amendment, and all documents executed and delivered herewith,
supersede all prior agreements and understandings relating to subject matter
hereof. This First Amendment together with the Loan Agreement, and the documents
executed and delivered in connection herewith and therewith shall be construed
as one agreement, and in the event of any inconsistency, the provisions of any
promissory note evidencing a portion of the Indebtedness shall control over the
provisions of this First Amendment.

               7.2 Counterparts. This First Amendment may be executed in any
number of counterparts and by different parties on separate counterparts, each
of which counterparts, when so executed and delivered, shall be deemed to be an
original and all of which counterparts, taken together, shall constitute but one
and the same instrument. This First Amendment shall be effective upon the
execution and delivery of a counterpart hereof by each of the parties hereto.

               7.3 Captions. The captions or headings in this First Amendment
are for convenience of reference only and in no way define, limit, or
circumscribe the scope or intent of any provision of this First Amendment.

               7.4 Successors and Assigns; Governing Law. This First Amendment
shall be binding upon and inure to the benefit of the respective parties hereto
and their successors and assigns and shall be governed by, and construed and
enforced in accordance with, the internal laws of the Commonwealth of
Pennsylvania without regard to its principles of conflicts of laws.




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         IN WITNESS WHEREOF, intending to be legally bound hereby, the
undersigned have executed this First Amendment as of the day and year first
written above.


                                UNITED STATES LIME & MINERALS, INC., as
                                Borrower

                                By: /s/ TIMOTHY W. BYRNE
                                   --------------------------------------------
                                   Name:  Timothy W. Byrne
                                        ---------------------------------------
                                   Title: President and Chief Executive Officer
                                         --------------------------------------


                                TEXAS LIME COMPANY, as Borrower


                                By: /s/ TIMOTHY W. BYRNE
                                   --------------------------------------------
                                   Name: Timothy W. Byrne
                                        ---------------------------------------
                                   Title:  President
                                         --------------------------------------


                                ARKANSAS LIME COMPANY, as Borrower


                                By: /s/ TIMOTHY W. BYRNE
                                   --------------------------------------------
                                   Name:  Timothy W. Byrne
                                        ---------------------------------------
                                   Title: President
                                         --------------------------------------


                                FIRST UNION NATIONAL BANK, as Administrative
                                Agent and Lender


                                By: /s/ STUART MACGREGOR
                                   --------------------------------------------
                                   Name:  Stuart MacGregor
                                        ---------------------------------------
                                   Title: V.P.
                                        ---------------------------------------

                                COMPASS BANK, as Lender


                                By: /s/ KAY COKER
                                   --------------------------------------------
                                   Name: Kay Coker
                                        ---------------------------------------
                                   Title:  Executive Vice President
                                         --------------------------------------


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                                MERCANTILE BANK OF ARKANSAS, NATIONAL
                                ASSOCIATION, as Lender


                                By:
                                   --------------------------------------------
                                   Name:
                                        ---------------------------------------
                                   Title:
                                         --------------------------------------


                                FIRST NATIONAL BANK, as Lender


                                By:
                                   --------------------------------------------
                                   Name:
                                        ---------------------------------------
                                   Title:
                                         --------------------------------------


                                MINNESOTA VALLEY BANK, as Lender


                                By: /s/ BRIAN M. MATGHE
                                   --------------------------------------------
                                   Name:  Brian M. Matghe
                                        ---------------------------------------
                                   Title: Vice President
                                         --------------------------------------


                                SAND RIDGE BANK, as Lender


                                By:       /s/ DAVID S. HARVEY
                                   --------------------------------------------
                                   Name:  David S. Harvey
                                        ---------------------------------------
                                   Title: EVP/CLO
                                         --------------------------------------




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                                BREMER BANK NATIONAL ASSOCIATION, as Lender


                                By: /s/  DIANE M. PAVDUHN
                                   --------------------------------------------
                                   Name: Diane M. Pavduhn
                                        ---------------------------------------
                                   Title: Officer
                                         --------------------------------------


                                DANVILLE STATE BANK, as Lender


                                By: /s/ PHILIP ALEXANDER
                                   --------------------------------------------
                                   Name: Philip Alexander
                                        ---------------------------------------
                                   Title: Senior V.P.
                                         --------------------------------------


                                FIRST BANKERS TRUST COMPANY, NATIONAL
                                ASSOCIATION, as Lender


                                By:  /s/ TOMMY W. LAY
                                   --------------------------------------------
                                   Name:  Tommy W. Lay
                                        ---------------------------------------
                                   Title: Vice President
                                        ---------------------------------------


                                SECURITY STATE BANK, as Lender


                                By: /s/ MARK GARDESKI
                                   --------------------------------------------
                                   Name:  Mark Gardeski
                                        ---------------------------------------
                                   Title: Vice President
                                         --------------------------------------


                                ACKLEY STATE BANK, as Lender


                                By: /s/ KENT L. STASLAND
                                   --------------------------------------------
                                   Name: Kent L. Stasland
                                        ---------------------------------------
                                   Title: EVP
                                         --------------------------------------


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                                INTEGRITY BANK PLUS, as Lender


                                By: /s/ CHARLES J. ROBASSE
                                   --------------------------------------------
                                   Name:  Charles J. Robasse
                                        ---------------------------------------
                                   Title: Chairman
                                         --------------------------------------


                                FIRST STATE BANK OF OKABENA, INC., as Lender


                                By:   /s/ DENNIS P. HARTMAN
                                   --------------------------------------------
                                   Name:  Dennis P. Hartman
                                        ---------------------------------------
                                   Title: President
                                         --------------------------------------



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                                                                    EXHIBIT "A"



                       [Attach form of Subordinated Note]