<PAGE>   1
 
                                  SCHEDULE 14A
                                 (RULE 14A-101)
 
                    INFORMATION REQUIRED IN PROXY STATEMENT
 
                            SCHEDULE 14A INFORMATION
 
          PROXY STATEMENT PURSUANT TO SECTION 14(A) OF THE SECURITIES
                EXCHANGE ACT OF 1934 (AMENDMENT NO.           )
 
     Filed by the Registrant [X]
     Filed by a Party other than the Registrant [ ]
     Check the appropriate box:
     [ ] Preliminary Proxy Statement       [ ] Confidential, for Use of the
                                               Commission Only (as permitted by
                                               Rule 14a-6(e)(2))
     [X] Definitive Proxy Statement
     [ ] Definitive Additional Materials
     [ ] Soliciting Material Pursuant to sec. 240.14a-11(c) or sec. 240.14a-12
                    
                     United States Lime & Minerals, Inc.
--------------------------------------------------------------------------------
                (Name of Registrant as Specified in its Charter)
                       
--------------------------------------------------------------------------------
    (Name of Person(s) Filing Proxy Statement, if other than the Registrant)
 
Payment of Filing Fee (Check the appropriate box):
     [X] No fee required.
     [ ] Fee computed on table below per Exchange Act Rules 14a-6(i)(l) and
         0-11.
 
     (1) Title of each class of securities to which transaction applies:
 
--------------------------------------------------------------------------------
     (2) Aggregate number of securities to which transaction applies:
 
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     (3) Per unit price or other underlying value of transaction computed
pursuant to Exchange Act Rule 0-11 (Set forth the amount on which the filing fee
is calculated and state how it was determined):
 
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     (4) Proposed maximum aggregate value of transaction:
 
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     (5) Total fee paid:
 
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     [ ] Fee paid previously with preliminary materials.
 
     [ ] Check box if any part of the fee is offset as provided by Exchange Act
Rule 0-11(a)(2) and identify the filing for which the offsetting fee was paid
previously. Identify the previous filing by registration statement number, or
the Form or Schedule and the date of its filing.
 
     (1) Amount Previously Paid:
 
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     (2) Form, Schedule or Registration Statement No.:
 
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     (3) Filing Party:
 
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     (4) Date Filed:
 
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<PAGE>   2
[UNITED STATES LIME & MINERALS, INC. LETTERHEAD]


                                      April 15, 1998


Dear Shareholders:

         You are cordially invited to attend the 1998 Annual Meeting of
Shareholders at 10:00 a.m. on Friday, May 15, 1998, at the Sheraton Park Central
Hotel, 12720 Merit Drive, Dallas, Texas 75251. Please refer to the back of this
letter for directions. The Meeting will be preceded by an informal reception
starting at 9:30 a.m., at which you will have an opportunity to meet the
Directors and Officers of the Company.

         Enclosed with this letter is a Notice of the Annual Meeting, Proxy
Statement, and Proxy Card. I urge you to complete, sign, date, and mail the
enclosed Proxy Card at your earliest convenience. Regardless of the size of your
holdings, it is important that your shares be represented. If you attend the
Meeting, you may withdraw your Proxy and vote in person.

         I look forward to meeting and speaking with you at the Annual Meeting
on May 15, 1998.

                                      Sincerely,

                                      /s/ TIMOTHY W. BYRNE

                                      Timothy W. Byrne
                                      President and Chief Executive Officer


Enclosures

<PAGE>   3

             Directions to the 1998 Annual Meeting of Shareholders

                      UNITED STATES LIME & MINERALS, INC.

                      Friday, May 15, 1998, at 10:00 a.m.


                                     [Map]
<PAGE>   4


                      UNITED STATES LIME & MINERALS, INC.
                                12221 Merit Drive
                                    Suite 500
                               Dallas, Texas 75251



                NOTICE OF THE 1998 ANNUAL MEETING OF SHAREHOLDERS

                           To Be Held On May 15, 1998




To the Shareholders of
         United States Lime & Minerals, Inc.:

         Notice is hereby given that the 1998 Annual Meeting of Shareholders of
United States Lime & Minerals, Inc., a Texas corporation (the "Company"), will
be held on Friday, the 15th day of May, 1998, at 10:00 a.m., local time at the
Sheraton Park Central Hotel, 12720 Merit Drive, Dallas, Texas 75251 (the "Annual
Meeting"), for the following purposes:

         1.       To elect five directors to serve until the next annual meeting
                  of shareholders and until their respective successors have
                  been duly elected and qualified; and
         2.       To transact such other business as may properly be brought
                  before the Annual Meeting or any adjournment thereof.


         Information regarding the matters to be acted upon at the Annual
Meeting is contained in the Proxy Statement accompanying this Notice.


         The Board of Directors has fixed the close of business on March 31,
1998 as the record date for the determination of shareholders entitled to notice
of and to vote at the Annual Meeting or any adjournment thereof. Only
shareholders of record at the close of business on the record date will be
entitled to notice of and to vote at the Annual Meeting or any adjournment
thereof. A complete list of such shareholders will be available for inspection
during usual business hours for ten days prior to the Annual Meeting at the
office of the Company in Dallas, Texas.


         All shareholders are cordially invited to attend the Annual Meeting.
SHAREHOLDERS ARE URGED, WHETHER OR NOT THEY PLAN TO ATTEND THE ANNUAL MEETING,
TO COMPLETE, SIGN, AND DATE THE ACCOMPANYING PROXY CARD AND TO RETURN IT
PROMPTLY IN THE POSTAGE-PAID RETURN ENVELOPE PROVIDED. If a shareholder who has
returned a Proxy Card attends the Annual Meeting in person, such shareholder may
revoke the Proxy and vote in person on all matters submitted to the shareholders
at the Annual Meeting.


                                 By the Order of the Board of Directors,



                                 Timothy W. Byrne,
                                 President, Chief Executive Officer & Secretary
Dallas, Texas
April 15, 1998


<PAGE>   5



                       UNITED STATES LIME & MINERALS, INC.
                                12221 MERIT DRIVE
                                    SUITE 500
                               DALLAS, TEXAS 75251


                                 PROXY STATEMENT
                                     FOR THE
                       1998 ANNUAL MEETING OF SHAREHOLDERS
                           TO BE HELD ON MAY 15, 1998


                                  INTRODUCTION


         The accompanying proxy (the "Proxy Card"), mailed together with this
proxy statement (the "Proxy Statement"), is solicited by and on behalf of the
Board of Directors of United States Lime & Minerals, Inc., a Texas corporation
(the "Company"), for use at the 1998 Annual Meeting of Shareholders of the
Company to be held at the time and place and for the purposes set forth in the
accompanying Notice (the "Annual Meeting"). The approximate date on which this
Proxy Statement and Proxy Card were first sent to shareholders of the Company is
April 15, 1998.

         Shares of the Company's common stock, par value $0.10 per share (the
"Common Stock"), represented by valid Proxies in the form enclosed, duly signed,
dated, and returned to the Company and not revoked, will be voted at the Annual
Meeting in accordance with the directions given. In the absence of directions to
the contrary, such shares will be voted:

                  FOR the election of the five nominees named in the Proxy Card
                  to the Board of Directors of the Company (the "Board of
                  Directors" or the "Board").

         If any other matter is properly brought before the Annual Meeting for
action at the Meeting, which is not currently anticipated, the Proxy holders
will vote the Proxies in accordance with their best judgment in such matters.

         Any shareholder of the Company returning a Proxy Card has a right to
revoke the Proxy at any time before it is exercised by giving written notice of
such revocation to the Company addressed to Timothy W. Byrne, President, Chief
Executive Officer and Secretary, United States Lime & Minerals, Inc., 12221
Merit Drive, Suite 500, Dallas, Texas 75251; however, no such revocation shall
be effective until such notice of revocation has been received by the Company at
or prior to the Annual Meeting.



                   VOTING SECURITIES AND PRINCIPAL SHAREHOLDER

         Only holders of record of Common Stock at the close of business on
March 31, 1998, the record date for the Annual Meeting, are entitled to notice
of and to vote at the Annual Meeting or any adjournment thereof. The presence of
the holders of a majority of the outstanding shares of Common Stock is necessary
to constitute a quorum. On the record date for the Annual Meeting, there were
issued and outstanding 3,969,425 shares of Common Stock. At the Annual Meeting,
each shareholder of record on March 31, 1998 will be entitled to one vote for
each share of Common Stock registered in such shareholder's name on the record
date.


<PAGE>   6



         The following table sets forth, as of March 31, 1998, information with
respect to the only shareholder known to the Company to be the beneficial owner
of more than five percent of the issued and outstanding shares of Common Stock:

<TABLE>

<CAPTION>

      Name and Address                                Number of Shares                    Percent
     of Beneficial Owner                             Beneficially Owned                  of Class
     -------------------                             ------------------                  --------

<S>                                                       <C>                             <C>    
Inberdon Enterprises Ltd.                                 2,013,448                       50.72 %
1020-789 West Pender Street
Vancouver, British Columbia
Canada V6C 1H2 (1)

</TABLE>

--------------------- 
(1)  Inberdon Enterprises Ltd. ("Inberdon") is principally engaged in the
     acquisition and holding of securities of aggregate producing companies
     located in North America. All of the outstanding shares of Inberdon are
     held, indirectly through a number of private companies, by Mr. George M.
     Doumet.



                              ELECTION OF DIRECTORS

         Five directors, constituting the entire Board of Directors, are to be
elected at the Annual Meeting to serve until the next annual meeting of
shareholders and until their respective successors have been duly elected and
qualified. All of the nominees are currently directors of the Company.

         Directors are elected by a plurality of the votes cast by the holders
of shares entitled to vote in the election of directors at the Annual Meeting.
The Company's Restated Articles of Incorporation prohibit cumulative voting for
the election of directors. All duly submitted and unrevoked Proxies will be
voted FOR the nominees selected by the Board of Directors except where
authorization so to vote is withheld. Abstentions and broker non-votes are not
counted in the election of directors.

         The Board of Directors recommends that all shareholders vote FOR the
election of all such nominees. If any nominee should become unavailable for
election for any presently unforeseen reason, the persons designated as Proxy
holders will have full discretion to vote for another person.

         The Company has a standing Executive Committee, Audit Committee, and
Compensation Committee, but does not have a standing nominating committee.
During the fiscal year ended December 31, 1997, the Board of Directors held five
meetings, and the Executive Committee held two meetings. The Audit Committee
held two meetings, and the Compensation Committee held one meeting. During the
fiscal year ended December 31, 1997, each director attended all meetings held by
the Board of Directors and the committees of the Board on which he served.

         The five nominees for director are named below. Each has consented to
serve as a director if elected. Set forth below is pertinent information with
respect to each nominee:

    JOHN J. BROWN

          Mr. Brown, age 65, has served as a director of the Company since July
          1993. Mr. Brown is the President of Pacific Opportunity Company, Ltd.,
          a management consulting and merchant banking firm located in
          Vancouver, Canada. He is a director and officer of several natural
          resources firms, including Key West Energy Corporation. From 1990 to
          1993, he served as a director and chief financial officer of BTS Byers
          Transportation Systems Inc., an `LTL' transportation firm in Western
          Canada. From 1984 to 1990, Mr. Brown was an investment advisor with a
          Canadian brokerage firm. Mr. Brown is a Chartered Accountant and was
          formerly a senior partner with the public auditing firm of Deloitte &
          Touche, Chartered Accountants, in Vancouver, Canada.

                                      -2-
<PAGE>   7



    TIMOTHY W. BYRNE

          Mr. Byrne, age 40, has served as a director of the Company since March
          1991. Mr. Byrne also currently serves as President and Chief Executive
          Officer of the Company, as well as Chief Financial Officer and
          Secretary. From December 1993 to December 1997, he served as Senior
          Vice President - Finance and Administration and Chief Financial
          Officer. Mr. Byrne joined the Company in August 1990 as Manager of
          Finance. From 1985 through 1989, Mr. Byrne was a partner in a
          Washington, D.C. consulting and accounting firm.


    ANTOINE M. DOUMET

          Mr. Doumet, age 38, has served as a director of the Company since July
          1993 in the capacity of Vice Chairman. He is a private businessman and
          investor. From 1989 to 1995, he served as a director of MELEC, a
          French electrical engineering and contracting company. From 1988 to
          1992, Mr. Doumet served as vice president and a director of Lebanon
          Chemicals Company. Mr. Doumet is the brother of Mr. George M. Doumet,
          who indirectly owns all of the outstanding shares of Inberdon.


    WALLACE G. IRMSCHER

          Mr. Irmscher, age 75, has served as a director of the Company since
          July 1993. He was a senior executive with 44 years of diversified
          experience in the construction and construction materials industry.
          Since 1995, he has served as a director of N-Viro International
          Corporation, a company involved in the recycling of industrial waste.
          From 1993 to 1995, Mr. Irmscher was a director and officer of
          Newfoundland Resources & Mining Company Limited. In 1995, a petition
          was filed against this company, and it was adjudged bankrupt. Mr.
          Irmscher for the past five years has performed consulting services for
          various companies in the cement, construction, and environmental
          industries.


    EDWARD A. ODISHAW

          Mr. Odishaw, age 62, has served as a director and Chairman of the
          Board of the Company since July 1993. He has practiced law in
          Saskatchewan and British Columbia, Canada since 1964, with emphasis on
          commercial law, corporate mergers, acquisitions and finance. Mr.
          Odishaw has been a Barrister and Solicitor with the law firm of
          Boughton Peterson Yang Anderson, located in Vancouver, Canada, since
          February 1992. From 1972 to 1992, Mr. Odishaw was a Barrister and
          Solicitor with the law firm of Swinton & Company, Vancouver, Canada.
          Mr. Odishaw holds directorships in numerous companies in Canada. Mr.
          Odishaw is a member in good standing of the Law Society of British
          Columbia and the Canadian Bar Association and is a non-practicing
          member of the Law Society of Saskatchewan.


                               EXECUTIVE OFFICERS
                           WHO ARE NOT ALSO DIRECTORS

    JOHNNEY G. BOWERS

              Mr. Bowers, age 51, joined the Company in June 1997 and serves as
    Vice President - Manufacturing. He brings over 25 years of engineering and
    operating experience to the Company. From 1991 until he joined the Company,
    Mr. Bowers served as director of engineering with Chemical Lime Company.
    Prior to 1991, Mr. Bowers held various senior process engineering and
    project manager positions in the mining and processing industry.


    LARRY T. OHMS

              Mr. Ohms, age 36, joined the Company in July 1994 as Corporate
    Controller. From 1990 until that time, Mr. Ohms served as vice president of
    finance for My Alarm, Inc., a manufacturer and distributor of two-way voice,
    home security systems. Prior to 1990, Mr. Ohms held positions as plant
    controller for publicly traded companies, including Flowers Baking Company
    and Weyerhauser Company.



                                      -3-

        
<PAGE>   8
    SHAREHOLDINGS OF COMPANY DIRECTORS AND EXECUTIVE OFFICERS

         The table below sets forth the number of shares of Common Stock
beneficially owned, as of March 31, 1998, by all directors and named executive
officers of the Company individually and all directors and current executive
officers as a group:

<TABLE>

<CAPTION>


                                                     Common Stock Beneficially Owned (1)
                                            ------------------------------------------------
                          Name                  Number of Shares            Percent of Class
                  ----------------------    -------------------------    -------------------
                  <S>                             <C>      <C>                      <C>  
                  John J. Brown                     -                                 -
                  Timothy W. Byrne                71,537   (2)(3)(4)                1.78%
                  Antoine M. Doumet                 -      (5)                        -
                  Wallace G. Irmscher              8,000                             (7)
                  Edward A. Odishaw               10,900                             (7)
                  Robert F. Kizer                 86,448   (6)                      2.16%

                  All Directors and
                  Current Executive Officers
                  as a Group (7 persons)          90,827   (2) (3) (4)              2.27%

</TABLE>

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

(1)  All shares are directly held with sole voting and dispositive power unless
     otherwise indicated.

(2)  The named individual serves as one of three members of the Company's
     Employee Stock Ownership Plan ("ESOP") Administration Committee. The number
     of shares shown as beneficially owned by the named individual excludes
     shares that may be deemed to be beneficially owned by the ESOP
     Administration Committee, as to which the named individual disclaims
     beneficial ownership.

(3)  Includes 6,537 and 390 shares allocated to Messrs. Byrne and Ohms,
     respectively, under the ESOP, as to which they have sole voting power but
     no dispositive power.

(4)  Includes 40,000 shares subject to stock options exercisable within the next
     60 days granted to Mr. Byrne under the Company's 1992 Stock Option Plan
     (the "1992 Plan").

(5)  The named individual is the brother of Mr. George M. Doumet, who indirectly
     owns all of the outstanding shares of Inberdon.

(6)  Mr. Kizer served as an executive officer until December 6, 1997, and as a
     director until March 6, 1998. Includes 1,086 shares allocated to Mr. Kizer
     under the ESOP, as to which he has sole voting power but no dispotive
     power. Also includes 40,000 shares subject to stock options exercisable
     within the next 60 days granted to Mr. Kizer under the 1992 Plan.

(7)  Less than 1%.

                                      -4-
<PAGE>   9



                             EXECUTIVE COMPENSATION
                           SUMMARY COMPENSATION TABLE

         The following table sets forth the cash and non-cash compensation for
each of the last three fiscal years earned by the current and former Chief
Executive Officers. No other executive officers of the Company earned salary and
bonus in 1997 that exceeded $100,000:

<TABLE>

<CAPTION>

                                                                 LONG-TERM
                                       ANNUAL COMPENSATION     COMPENSATION              ALL OTHER COMPENSATION
                                       -------------------     ------------              ----------------------
                                                                SECURITIES
         NAME AND                                               UNDERLYING
    PRINCIPAL POSITION       YEAR      SALARY       BONUS       OPTIONS (#)         401(K)        ESOP          OTHER
-------------------------   -------   ---------   ---------   --------------       ---------    ---------    --------
                                                                    (3)               (4)          (5)           (6)
<S>                          <C>       <C>         <C>              <C>              <C>             <C>         <C>   
Timothy W. Byrne             1997      $169,130    $20,000 (1)       -              $3,373          $2,094          -
President, Chief             1996      $168,833    $12,000 (2)       -              $3,857          $1,572          -
Executive Officer and        1995      $157,500    $37,500 (2)     25,000           $3,080          $7,340          -
Chief Financial Officer

Robert F. Kizer (7)          1997      $212,500    $20,000 (1)       -              $3,830          $1,544     $270,000
Former President and         1996      $213,518        -             -              $3,167          $1,000          -
Chief Executive Officer      1995      $206,667    $75,000 (2)     40,000           $3,080          $7,141          -

</TABLE>

-------------------- 
(1)  Bonuses based on executive officer's achievement of defined goals accrued
     and paid in the year shown.

(2)  Bonuses based on Company performance accrued in the year shown and paid in
     the following year.

(3)  Options granted pursuant to the 1992 Plan.

(4)  Company contribution to defined contribution plan.

(5)  ESOP share allocation, valued at the year-end market price of the Common
     Stock.

(6)  Termination payment accrued in 1997 and paid to Mr. Kizer in March 1998
     pursuant to employment agreement

(7)  Mr. Kizer served as an executive officer until December 6, 1997.




       AGGREGATE OPTION EXERCISES IN LAST YEAR AND YEAR-END OPTION VALUES

         The following table sets forth information with respect to stock
options exercised by the named executive officers during 1997 and the number and
value of unexercised options held by such executive officers at year end:

<TABLE>

<CAPTION>

                                                               Number of Securities             Value of Unexercised
                                                              Underlying Unexercised            In-the-Money Options
                                                              Options at Year-End (#)              at Year-End ($)
                         Shares Acquired        Value     ------------------------------  -----------------------------
        Name            on Exercise (#)    Realized ($)   Exercisable      Unexercisable  Exercisable     Unexercisable
--------------------  ------------------  -------------   -----------      -------------  -----------     -------------
<S>                         <C>                 <C>           <C>               <C>            <C>               <C>   
Timothy W. Byrne               -                 -             40,000             -          39,375                -
Robert F. Kizer (1)            -                 -             77,210             -          97,676                -

</TABLE>

--------------------
(1)  Mr. Kizer served as an executive officer until December 6, 1997. Mr. Kizer
     exercised options for 37,210 shares in March 1998.


                                      -5-
<PAGE>   10

                 EXECUTIVE EMPLOYMENT AND TERMINATION AGREEMENTS

         The Company has employment agreements with Messrs. Byrne and Bowers.
Such employment agreements are designed to ensure that the Company will be able
to attract, motivate, and retain highly qualified talent, which is critical to
both the short- and long-term success of the Company.

         The agreements provide for an annual base salary to be reviewed
annually. In addition to the base salary, the agreements provide for a bonus (to
be determined by the Compensation Committee of the Board of Directors), use of a
Company car, reimbursement of business expenses, and participation in the
Company's 401(k) plan and ESOP. In case of termination of employment, including
upon a change in control, Mr. Byrne would receive a severance payment equal to
eighteen months' compensation, and the severance payment would be six months'
compensation in the case of Mr. Bowers. Mr. Byrne's agreement contains certain
post-termination covenants not to compete. Messrs. Byrne's and Bowers'
agreements have no expiration date.

         In December 1997, the Company terminated Mr. Kizer's employment
agreement. Mr. Kizer's employment agreement provided for a severance payment
equal to one year's compensation and benefits. In February 1998, the Company and
Mr. Kizer agreed to a Mutual Release Agreement, and, in March 1998, the Company
paid Mr. Kizer an agreed-upon termination payment of $270,000. Mr. Kizer's
employment agreement contained certain post-termination covenants not to
compete.


                   COMPENSATION OF DIRECTORS AND OTHER MATTERS

         Directors who are not employees of the Company, other than the Chairman
of the Board of Directors, are paid an annual retainer of $11,000 plus $600 per
day on Company business. The Chairman of the Board is paid an annual retainer of
$40,000 plus $800 per day on Company business.

         The Company had entered into a consulting agreement with Mr. Irmscher
for $2,000 per month, commencing April 1996. Pursuant to the agreement, Mr.
Irmscher aided the Company in pursuing acquisitions and expansion opportunities.
The agreement was not renewed in April 1998.


                                      -6-
<PAGE>   11


                      REPORT OF THE COMPENSATION COMMITTEE


TO:      The Shareholders of United States Lime & Minerals, Inc.

         As members of the Compensation Committee of the Board of Directors (the
"Committee"), we have the responsibility for administering the executive
compensation program of the Company. The Compensation Committee reviews and
makes recommendations to the full Board of Directors regarding the base salaries
and annual incentive compensation for executive officers and administers the
Company's 1992 Stock Option Plan. The Compensation Committee is composed of
Messrs. Odishaw, Doumet, and, since May 1997, Irmscher.


COMPENSATION POLICIES

         The principal executive compensation policy of the Company, which is
endorsed by the Committee, is to provide a compensation program that will
attract, motivate, and retain persons of high quality and will support a
long-standing internal culture of loyalty and dedication to the interests of the
Company and its shareholders. In administering the executive compensation
program, the Committee is mindful of the following principles and guidelines
which are supported by the full Board:

         Base salaries for executive officers should be competitive. A
sufficient portion of annual compensation should be at risk in order to align
the interests of executives with those of the shareholders of the Company. This
variable part of annual compensation should reflect both individual and
corporate performance. As a person's level of responsibility increases, a
greater portion of total compensation should be at risk, and the mix of total
compensation should be weighted more heavily in favor of stock-based
compensation. Stock options provide executives long-term incentive and help
align the interests of executives and shareholders in the enhancement of
shareholder value.

         As discussed elsewhere in this Proxy Statement, the Company has entered
into employment agreements with Messrs. Byrne and Bowers. These agreements
provide for an annual base salary, bonus, the use of a Company car,
reimbursement of business expenses, participation in the 401(k) plan and ESOP,
and severance arrangements. The Committee has determined that such agreements
are appropriate means to achieve the Company's overall compensation policies.


1997 COMPENSATION

         The Company's executive compensation packages have three separate
elements, consisting of base salary, annual incentive compensation, and
long-term incentive compensation. The compensation packages of Mr. Byrne and the
other executive officers are designed to be competitive within the industry and
to provide incentives for both short- and long-term performance in line with the
financial interests of the shareholders.

BASE SALARIES. The Committee determined levels of the executive officers' base
salaries so as to be competitive with amounts paid to executives performing
similar functions in comparable size non-durable manufacturing companies. The
amount of each executive's annual increase in base salary, if any, will be based
on a number of largely subjective factors, including the personal performance of
such executive officer, the performance of the Company, cost-of-living
increases, and such other factors as the Committee deems appropriate, including
the individual's overall mix between fixed and variable compensation and between
cash and stock-based compensation. In November 1997, Messrs. Byrne and Kizer
received salary increases of 9.1% and 7.1%, respectively; they had not received
salary increases since November 1995. 


                                      -7-
<PAGE>   12

ANNUAL INCENTIVE COMPENSATION. Each of the Company's executive officers is
eligible to receive annual cash bonus awards based on determinations made by the
Committee. The Company has not adopted a formal annual bonus plan. Rather, the
determination to pay a cash bonus, if any, is based on the Committee's
subjective judgment with respect to the past performance of the individual, or
on the individual's attainment of objective performance goals set by the
Committee. In either such case, the bonus may be based on the specific
accomplishments of the individual, or on the overall success of the Company. In
November 1997, the Committee awarded special bonuses to Messrs. Byrne and Kizer
of $20,000 each based on the achievement of certain performance goals related to
the sale of substantially all of Corson Lime Company's assets; in the view of
the Committee, such bonus awards were an appropriate means to reward the named
executive officers for their performance. No bonuses were awarded for the
Company's 1997 operating results.

LONG-TERM INCENTIVE COMPENSATION. The Committee also administers the Company's
1992 Stock Option Plan to provide long-term incentives to the Company's key
employees, including executive officers. Grants are based on each individual's
position within the Company, level of responsibility, past performance, and
expectation of future performance. No options were granted in 1997. At the end
of 1997, Mr. Byrne held options to purchase 40,000 shares of Common Stock and
Mr. Kizer held options to purchase 77,210 shares of Common Stock.

         The Committee has not formally considered or adopted a policy with
regard to qualifying bonus awards and future stock option grants for tax
deductibility under Internal Revenue Code Section 162(m), which generally limits
the corporate tax deduction for compensation paid to certain named executive
officers to $1 million per year. The Committee has not yet seen the need to
address this issue, since current Company cash compensation is well below the
level at which this new tax limitation would apply, and the Company's stock
option grants made to date are not subject to the limitation.

         This report shall not be deemed to be incorporated by reference by any
general statement incorporating by reference the Proxy Statement into any filing
under the Securities Act of 1933 or the Securities Exchange Act of 1934, except
to the extent that the Company specifically incorporates this information by
reference. This report shall not otherwise be deemed to be filed under such
Acts.

                                              COMPENSATION COMMITTEE



                                              Edward A. Odishaw
                                              Antoine M. Doumet
                                              Wallace G. Irmscher


                                      -8-
<PAGE>   13



                                PERFORMANCE GRAPH


         The graph below compares the cumulative five-year total shareholders'
return on the Company's Common Stock with the cumulative total return on the
Nasdaq Market Index and a group of peer issuers selected on a line-of-business
basis, consisting of Dravo Corporation and A.P. Green Industries, Inc. The graph
assumes that the value of the investment in the Common Stock and each index was
$100 on December 31, 1992, and that all dividends have been reinvested.


          Comparison of Cumulative Five-Year Total Shareholders' Return


                                    [Chart]

<TABLE>

<CAPTION>


-------------------------------------------------------------------------------------------------------------------
         DECEMBER 31,          1992           1993            1994           1995           1996            1997
-------------------------------------------------------------------------------------------------------------------
         <S>                 <C>             <C>            <C>             <C>            <C>            <C>    
         COMPANY             $100.00         $133.33        $160.00         $235.83        $238.23        $203.44
         NASDAQ              $100.00         $119.95        $125.94         $163.35        $202.99        $248.30
         PEER GROUP          $100.00         $136.61        $144.28         $149.44        $168.34        $151.27
-------------------------------------------------------------------------------------------------------------------

</TABLE>


                              INDEPENDENT AUDITORS

         The firm of Ernst & Young LLP (a limited liability partnership) audited
the financial statements of the Company for the fiscal year ended December 31,
1997. Representatives of Ernst & Young LLP are expected to be present at the
Annual Meeting and to be available to respond to appropriate questions. Such
representatives will be given the opportunity to make a statement at the Meeting
if they so desire.

         The Audit Committee of the Board of Directors is currently composed of
Messrs. Brown and Irmscher. The Audit Committee recommends the appointment of
the independent auditors to audit the Company's financial statements, meets with
the independent auditors and reviews the scope and results of their audit, and
reviews the fees charged by the independent auditors.

         Ratification of independent auditors by the shareholders is not
required by Texas law or the Restated Articles of Incorporation or Bylaws of the
Company.


                                      -9-
<PAGE>   14


                                  OTHER MATTERS

         The Board of Directors does not intend to present any other matters at
the Annual Meeting and knows of no other matters that will be presented.
However, if any other matters properly come before the Annual Meeting, the
persons named in the enclosed Proxy Card intend to vote thereon in accordance
with their best judgment.


                              SHAREHOLDER PROPOSALS

         Shareholder proposals to be presented at the 1999 Annual Meeting of
Shareholders must be received by the Company at its office in Dallas, Texas
addressed to Timothy W. Byrne, President, Chief Executive Officer and Secretary
of the Company, not later than December 16, 1998.

         The costs of solicitation of Proxies will be borne by the Company.
Solicitation may be made by mail, personal interview, telephone, and/or
telegraph by officers and regular employees of the Company who will receive no
additional compensation therefor. The Company may specifically engage a firm to
aid in the solicitation of Proxies, for which services the Company would
anticipate paying a standard reasonable fee plus out-of-pocket expenses. The
Company will bear the reasonable expenses incurred by banks, brokerage firms,
and other custodians, nominees, and fiduciaries in forwarding proxy materials to
beneficial owners.


                                      UNITED STATES LIME & MINERALS, INC.




                                      TIMOTHY W. BYRNE,
Dallas, Texas                          President, Chief Executive Officer
April 15, 1998                           and Secretary


                                      -10-
<PAGE>   15
PROXY

                       UNITED STATES LIME & MINERALS, INC.
                                        
              Proxy Solicited on Behalf of the Board of Directors

The undersigned hereby appoints Edward A. Odishaw and Timothy W. Byrne, and
either of them, Proxies, with power of substitution in each, and hereby
authorizes them to represent and to vote, as designated below, all shares of
Common Stock of UNITED STATES LIME & MINERALS, INC. standing in the name of the
undersigned on March 31, 1998, at the Annual Meeting of Shareholders to be held
on May 15, 1998, at the Sheraton Park Central Hotel, 12720 Merit Drive, Dallas,
Texas 75251, and at any adjournment thereof and especially to vote on the item
of business specified below, as more fully described in the Notice of the
Meeting dated April 15, 1998, and the Proxy Statement accompanying the same,
the receipt of which is hereby acknowledged.

                                      (change of address)

                                 -----------------------------------------------
1. Election of Directors,
   Nominees:                     -----------------------------------------------

   John J. Brown, Timothy W.     -----------------------------------------------
   Byrne, Antoine M. Doumet,
   Wallace G. Irmscher, and      -----------------------------------------------
   Edward A. Odishaw.            (If you have written in the above space, please
                                 mark the corresponding box on the reverse side
                                 of this card.)

You are encouraged to specify your choice by marking the           -------------
appropriate box, SEE REVERSE SIDE, but you need not mark            SEE REVERSE
any box if you wish to vote in accordance with the Board                SIDE
of Directors' recommendations.  The Proxies cannot vote            -------------
your shares unless you sign, date and return this Card.





4064 -- United States Lime & Minerals, Inc.
<PAGE>   16
                      UNITED STATES LIME & MINERALS, INC.
   PLEASE MARK VOTE IN OVAL IN THE FOLLOWING MANNER USING DARK INK ONLY. [ ]

1. Election of Directors --         For      Withhold       For All
                                    All        All          Except

                                    [ ]        [ ]           [ ]

For, except vote witheld from the following nominee(s):


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

In their discretion, the Proxies are authorized to vote upon such other
business as may properly be brought before the Meeting or any adjournment
thereof.

Attend Meeting           [ ]


Change of Address        [ ]


                                     Dated: ________________________, 1998


                                     Signature(s)________________________

                                     ____________________________________
                                     NOTE: Please sign exactly as name 
                                     appears hereon. Joint Owner should 
                                     When signing as an attorney, executor,
                                     administrator, trustee or guardian, 
                                     please give full title as such.





                               FOLD & DETACH HERE

                                        
                            YOUR VOTE IS IMPORTANT!
                                        
                PLEASE SIGN, DATE AND RETURN THIS CARD PROMPTLY
                          USING THE ENCLOSED ENVELOPE.





4064 -- United States Lime & Mineral, Inc.