<PAGE>   1
                               UNITED STATES
                    SECURITIES AND EXCHANGE COMMISSION
                         Washington, D.C.  20549

                                 Form 10-Q

(Mark One)
[ X ]      QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(d) OF
                   THE SECURITIES EXCHANGE ACT OF 1934

               For the quarterly period ended March 31, 1998

                                     OR

[   ]           TRANSITION REPORT PURSUANT TO SECTION 13 OR
                15(d) OF THE SECURITIES EXCHANGE ACT OF 1934

             For the transition period from ........ to ........

                     Commission file number is 0-4197


                    UNITED STATES LIME & MINERALS, INC.
          (Exact name of registrant as specified in its charter)

             TEXAS                                           75-0789226
   -------------------------------                   -------------------------
   (State or other jurisdiction of                       (I.R.S. Employer
    incorporation or organization)                        Identification No.)

12221 Merit Drive, Suite 500, Dallas, TX                        75251
----------------------------------------             -------------------------
(Address of principal executive offices)                      (Zip Code)

                              (972) 991-8400
            ----------------------------------------------------  
            (Registrant's telephone number, including area code)

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 (or for such shorter period that the 
registrant was required to file such reports), and  (2) has been subject to
such filing requirements for the past 90 days.
     Yes [ X ]      No [   ]

Indicate the number of shares outstanding of each of the issuer's classes of
common stock, as of the latest practicable date:  As of April 27, 1998, 
3,969,425 shares of common stock, $.10 par value, were outstanding.

<PAGE>   2
PART I.   FINANCIAL INFORMATION
ITEM 1:   FINANCIAL STATEMENTS

UNITED STATES LIME & MINERALS, INC. AND SUBSIDIARIES
CONDENSED CONSOLIDATED BALANCE SHEETS
(In thousands of dollars)
(Unaudited)
<TABLE>
<CAPTION>
                                                    March 31,    December 31,
                                                      1998           1997 
ASSETS                                              --------       --------
<S>                                                <C>            <C>
Current Assets:
  Cash and cash equivalents                        $  1,504       $  2,787
  Trade receivables, net                              4,113          3,624
  Inventories                                         3,327          3,001
  Prepaid expenses and other assets                     105            111  
                                                    --------       --------
     Total current assets                             9,049          9,523

Property, plant and equipment at cost                57,481         52,302
  Less:  Accumulated depreciation and depletion     (31,535)       (30,896)
                                                    --------       --------
  Property, plant and equipment, net                 25,946         21,406

Deferred tax assets, net                              2,505          2,537
Other assets, net                                        46             54  
                                                    --------       --------
     Total assets                                  $ 37,546       $ 33,520
                                                    ========       ========

LIABILITIES AND STOCKHOLDERS' EQUITY
Current Liabilities:
  Current installments of long-term debt           $  1,607       $  1,071
  Accounts payable                                    2,608          4,437
  Accrued expenses                                    1,340          1,594  
                                                    --------       --------
     Total current liabilities                        5,555          7,102

Long-term debt, excluding current installments        7,536          2,167
Other liabilities                                       101            101  
                                                    --------       --------
      Total liabilities                              13,192          9,370

Stockholders' Equity:
  Common stock                                          529            529
  Additional paid-in-capital                         14,949         15,135
  Retained earnings                                  22,933         22,729  
                                                    --------       --------
                                                     38,411         38,393
Less treasury stock at cost; 1,324,640 and
  1,342,212 shares of common stock, respectively    (14,057)       (14,243) 
                                                    --------       --------
     Total stockholders' equity                      24,354         24,150
                                                    --------       --------
     Total liabilities and stockholders' equity    $ 37,546       $ 33,520  
                                                    ========       ========
</TABLE>
    See accompanying notes to condensed consolidated financial statements.
                                      2
<PAGE>   3
UNITED STATES LIME & MINERALS, INC. AND SUBSIDIARIES
CONDENSED CONSOLIDATED STATEMENTS OF OPERATIONS
(In thousands of dollars, except per share data)
(Unaudited)
<TABLE>
<CAPTION>
                                              THREE MONTHS ENDED MARCH 31, 
                                         -------------------------------------
                                               1998                 1997
                                         ----------------     ----------------
<S>                                     <C>       <C>        <C>       <C>
Revenues                                $  6,469  100.0%     $  7,808  100.0%

Cost of revenues:
  Labor and other operating expenses       4,527   70.0%        6,233   79.8%
  Depreciation, depletion & amortization     666   10.3%          980   12.6%  
                                         ----------------     ----------------
                                           5,193   80.3%        7,213   92.4%
                                         ----------------     ----------------
Gross profit                               1,276   19.7%          595    7.6%

  Selling, general &
     administrative expenses                 926   14.3%        1,116   14.3%
                                         ----------------     ----------------
Operating profit (loss)                      350    5.4%         (521)  (6.7%)

  Other deductions (income):
    Interest expense                           3    0.0%          133    1.7%
    Other, net                               (74)  (1.1%)         (44)  (0.6%)
                                         ----------------     ----------------
                                             (71)  (1.1%)          89    1.1%
                                         ----------------     ----------------
Net income (loss) before income taxes        421    6.5%         (610)  (7.8%) 
                                         ----------------     ----------------
Federal and state income
    tax expense (benefit)                    118    1.8%         (122)  (1.5%)
                                         ----------------     ----------------
  Net income (loss)                     $    303    4.7%     $   (488)  (6.3%)
                                         ================     ================

Income (loss) per share of common stock:
  Basic earnings (loss)/common share    $    0.08            $  (0.12)
                                         =========            =========
  Diluted earnings (loss)/common share  $    0.08            $  (0.12)
                                         =========            =========
</TABLE>




   See accompanying notes to condensed consolidated financial statements.








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<PAGE>   4
UNITED STATES LIME & MINERALS, INC. AND SUBSIDIARIES
CONDENSED CONSOLIDATED STATEMENTS OF CASH FLOWS
(In thousands of dollars)
(Unaudited)
<TABLE>
<CAPTION>
                                                       THREE MONTHS ENDED
                                                            MARCH 31,
                                                    -----------------------
                                                      1998           1997
                                                    --------       --------
<S>                                                <C>            <C>
CASH FLOWS FROM OPERATING ACTIVITIES:
  Net income (loss)                                $    303       $   (488)
  Adjustments to reconcile net income to net cash
        used in operating activities:
    Depreciation, depletion & amortization              686          1,023
    Deferred income tax benefit                          32            -    
    Amortization of financing costs                     -               25
    Loss (gain) on sale of
      property, plant & equipment                         1             (5)
    Current assets (net change)  [1]                   (809)          (188)
    Other assets                                          8            (22)
    Current liabilities (net change)  [2]            (2,083)          (640)
    Other liabilities                                   -               (1)
                                                    --------       --------
    Net cash used in operating activities            (1,862)          (296)

CASH FLOWS FROM INVESTING ACTIVITIES:
  Purchase of property, plant & equipment            (5,228)        (1,681)
  Proceeds from sale of property, plant & equipment       1              5  
                                                    --------       --------
    Net cash used in investing activities            (5,227)        (1,676)

CASH FLOWS FROM FINANCING ACTIVITIES:
  Payment of common stock dividends                     (99)           (99)
  Proceeds from borrowings on term loan               6,000            -
  Principal payments on debt                            (95)          (286)
    Net cash provided by (used in)                  --------       --------
      financing activities                            5,806           (297)
                                                    --------       --------
  Net decrease in cash                               (1,283)        (1,137)
    Cash at beginning of period                       2,787          1,161  
                                                    --------       --------
    Cash at end of period                          $  1,504       $     24  
                                                    ========       ========

  Supplemental cash flow information:
    Interest paid                                  $    125       $    109  
                                                    ========       ========
    Income taxes paid                              $    -         $    219
                                                    ========       ========
</TABLE>
[1]  Exclusive of net change in cash
[2]  Exclusive of net change in current portion of debt



    See accompanying notes to condensed consolidated financial statements


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<PAGE>   5
             UNITED STATES LIME & MINERALS, INC. AND SUBSIDIARIES
             Notes to Condensed Consolidated Financial Statements
                                (Unaudited)

1.  Basis of Presentation
    ---------------------
    The condensed consolidated financial statements included herein have been
    prepared by the Company without independent audit.  In the opinion of the 
    Company's management, all adjustments of a normal and recurring nature 
    necessary to present fairly the financial position, results of operations 
    and cash flows for the periods presented have been made.  Certain 
    information and footnote disclosures normally included in financial 
    statements prepared in accordance with generally accepted accounting 
    principles have been condensed or omitted.  It is suggested that these 
    condensed consolidated financial statements be read in conjunction with
    the consolidated financial statements and notes thereto included in the 
    Company's Annual Report on Form 10-K for the period ended December 31, 
    1997.  The results of operations for the period ended March 31, 1998 are 
    not necessarily indicative of operating results for the full year.

2.  Inventories
    -----------
    Inventories consisted of the following at:
<TABLE>
<CAPTION>
     (In thousands of dollars)                      March 31,    December 31,
                                                      1998           1997 
                                                    --------       --------
<S>                                                <C>            <C>
        Lime and limestone inventories:
           Raw materials                           $    999       $    624
           Finished goods                               800            844  
                                                    --------       --------
                                                      1,799          1,468
           Service parts                              1,528          1,533  
                                                    --------       --------
              Total inventories                    $  3,327       $  3,001
                                                    ========       ========
</TABLE>
3.  Long-Term Debt
    --------------
    The Company has a financing agreement with a commercial bank.  The
    agreement, as amended and restated in December 1997, provides for a 
    $15,000,000 five-year secured term loan and a $4,000,000 unsecured 
    revolving credit facility which matures in December 1999.  Both loans bear 
    interest at the bank's prime rate but may, at the option of the Company,
    be converted into LIBOR-based loans that bear interest at LIBOR plus 1.65%
    for the term loan and LIBOR plus 1.5% for the revolving credit facility.
    The agreement also allows the Company to modify the interest
    characteristics of all or a portion of the outstanding loans by
    establishing a fixed rate with the bank or through the use of interest
    rate protection agreements with the bank.  In the first quarter of 1998,
    the Company elected the LIBOR-based interest option for the debt
    outstanding under the term loan.







                                      5
<PAGE>   6
    A summary of long-term debt is as follows:
<TABLE>
<CAPTION>
          (In thousands of dollars)                 March 31,    December 31,
                                                      1998           1997  
                                                    --------       --------
<S>                                                <C>            <C>
          Term loan                                $  9,143          3,238
          Revolving credit facility                     -              -     
                                                    --------       --------
             Subtotal                                 9,143          3,238
          Less current installments                   1,607          1,071  
                                                    --------       --------
                Long-term debt, excluding
             current installments                  $  7,536          2,167  
                                                    ========       ========
</TABLE>
    The additional amounts borrowed in the first quarter of 1998 were used to 
    partially fund the modernization and expansion project at the Texas 
    facility.  Interest costs of $101,000 were capitalized as part of the
    Texas project in the first quarter of 1998.

    The carrying amount of the Company's long-term debt approximates its fair
    value.

4.  Subsequent Event
    ----------------
    In April 1998, the Company entered into an interest rate protection
    agreement with its bank (the "Swap Agreement") to modify the interest 
    characteristics of $9,000,000 of its then outstanding debt from a variable
    rate to a fixed rate.  The Swap Agreement involves the exchange of
    interest obligations based on a fixed rate of 7.45% for interest
    obligations based on variable 30 day LIBOR rates over the five-year life
    of the Swap Agreement without an exchange of notional amounts upon which
    such interest obligations are based.  The interest rate differential to be
    paid or received as rates change will be accrued and recognized as an
    adjustment to interest expense.  The related amount payable to or
    receivable from the bank will be included as an adjustment to accrued
    expenses.  To the extent amounts are not material, the fair value of the
    Swap Agreement and changes in the fair value as a result of changes in
    market interest rates will not be recognized in the financial statements.

    In the event of the early termination of the debt obligation, or an early
    termination of the Swap Agreement, any realized gain or loss from the Swap 
    Agreement would be recognized as an adjustment to interest expense.















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<PAGE>   7
ITEM 2.   MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL
          CONDITION AND RESULTS OF OPERATIONS

Liquidity and Capital Resources
-------------------------------
     Net cash used in operating activities was $1,862,000 for the three
months ended March 31, 1998, as compared to $296,000 used in operating
activities for the three months ended March 31, 1997.  The increase in net
cash used in operating activities was primarily attributable to the payment of
certain invoices related to the modernization and expansion project at the
Texas facility that were included in accounts payable at December 31, 1997.

     The Company made $5,228,000 in capital expenditures in the first three
months of 1998, compared to $1,681,000 for the same period last year.  Of the 
1998 capital expenditures, approximately $4,600,000 were related to the 
modernization and expansion project at the Texas facility.  The Texas project 
includes the installation of a new stone crushing and handling system, the 
addition of a preheater to one of the existing kilns, additional storage, 
screening and shipping capacity and a new support building which will house a 
laboratory, administrative offices and shop facilities.

     The Texas improvements should allow the Company to better serve its
customers by improving both quality and service.  With the improvements, the 
Company expects to be in a better position to compete for customers who 
currently cannot use the Company's lime in their processes.  The improvements 
will also result in lower operating costs and in a more efficient utilization 
of the work force.  The cost of the Texas modernization and expansion project 
is expected to be approximately $22,000,000.  Although delays or changes in 
the cost of the project could occur due to inclement weather, changes in the 
design or cost overruns, none is anticipated at this time.  This project is 
being financed through a combination of internally generated funds from 
operations, the proceeds from the sale of substantially all of the Corson Lime 
Company assets and certain banking facilities.

     The Texas project is being constructed in phases and significant
progress has been made.  The new support building has been completed and the 
stone crushing and handling system should be completed by the second quarter 
of 1998.  The storage, screening and load-out improvements as well as the 
preheater should be completed by the fourth quarter of 1998.  The Company has 
secured all the necessary permits for construction.

     A similar modernization and expansion project has also been approved for
the Arkansas facility.  The Arkansas project will be constructed in two 
phases.  The first phase, scheduled for completion in 1999, includes the 
addition of a new 1,200-ton per day rotary kiln, a new stone crushing and 
handling system and new lime and ground calcium carbonate storage and load-out 
facilities.  The second phase of the project includes a new hydrator, a rock 
transportation system and additional lime storage facilities.  The second 
phase of the project is currently scheduled for construction in 2002.  
However, significant increases in product sales could result in an earlier 
implementation of the second phase of the plan.  Kiln system design and permit 
applications are currently being finalized and bid proposals have been 
requested for key components of the project.  The preliminary cost estimates 
for the project phases are approximately $27,000,000 and $5,000,000, 
respectively.  The project is contingent upon satisfactory permitting from the 



                                      7
<PAGE>   8
various regulatory agencies.  The Company expects to finance this project
through a combination of internally generated funds from operations and/or 
alternative sources of financing.

     The Arkansas improvements should allow the Company to better serve its
customers by improving both quality and service while increasing the 
production capacity of quicklime and hydrated lime.  With the improvements, 
the Company expects to be in a better position to compete for customers who 
currently cannot use the Company's lime in their processes due to insufficient 
production capacity at the plant or quality constraints. The new rotary kiln 
will have lower operating costs and a greater capacity than the six shaft 
kilns currently in use.  In addition to increasing capacity, this kiln will 
also be able to consistently produce high-quality lime for use by certain 
manufacturing customers who currently do not buy lime from the Arkansas 
facility.  The new stone crushing system will allow the Company to increase 
quarry capacity and produce aggregate products with materials that are not 
suitable for the production of lime.  This system will be designed to produce 
the appropriate size feed for the rotary kiln and will increase handling and 
transport capacity while significantly reducing labor requirements.  The new 
hydrator will increase capacity and produce hydrated lime more efficiently 
than the current systems.  The storage, screening and load-out facilities will 
also substantially reduce the amount of time required for the loading of bulk 
quicklime trucks and railcars.  The planned modernization and expansion 
project will increase both production and shipping capacity, will lower 
operating costs and will allow for a more efficient utilization of the work 
force.

     The Company is not contractually committed to any planned capital
expenditures until actual orders are placed for equipment.  As of March 31, 
1998, the Company's liability for open equipment and construction orders, all 
of which were related to the Texas modernization and expansion project, 
totaled approximately $2,600,000.  This amount, as well as other future 
billings related to the Texas and Arkansas modernization and expansion 
projects, will be recorded as work is performed and billed to the Company.

     As of March 31, 1998, the Company had approximately $9,143,000 in total
debt outstanding under the amended and restated term loan, up from the
$3,238,000 at December 31, 1997.  The additional borrowings in 1998 have been
used to partially fund the modernization and expansion project at the Texas
facility.


















                                      8
<PAGE>   9
Results of Operations
---------------------
     Revenues decreased from $7,808,000 in the first quarter of 1997 to
$6,469,000 in the first quarter of 1998, a decrease of $1,339,000, or 17.1%.  
Excluding 1997 revenues from Corson, revenues for the three months ended March 
31, 1998 increased by $560,000, or 9.5%, from 1997, resulting from a 9.9% 
increase in sales volume, primarily at the Texas facility, which was partially 
offset by 0.4% decrease in prices.

     The Company's gross profit was $1,276,000 in the first quarter of 1998,
compared to $595,000 in the first quarter of 1997, a 114.5% increase.  Gross 
profit margin as a percentage of revenues for the first quarter of 1998 
increased to 19.7% from 7.6% in 1997. The improved gross profit and gross 
profit margins were attributable to eliminating the high production costs at 
the Corson facility.  The favorable impact resulting from the elimination of 
the Corson operations was partially offset by higher fuel costs in 1998 at 
both the Texas and Arkansas facilities.

     Selling, general and administrative expenses ("SG&A") decreased by
$190,000, or 17.0%, to $926,000 in the first quarter of 1998, as compared to 
$1,116,000 in the first quarter of 1997.  The SG&A decrease was primarily 
attributable to the shut down of the Corson operations after the sale in June 
1997.  As a percent of sales, SG&A remained constant at 14.3%.

     Interest expense in the first quarter of 1998 was $3,000 as compared to
$133,000 in 1997.  This decrease was attributable to the capitalization of 
substantially all interest costs as part of the Texas modernization and 
expansion project.  Interest costs of approximately $101,000 were capitalized 
in the first quarter of 1998.

     The Company reported net income of $303,000 ($0.08 per share) during the
first quarter of 1998, compared to a net loss of $488,000 ($0.12 per share) 
during the first quarter of 1997.  Net income for the quarter was favorably 
impacted by the elimination of high production costs at Corson and increased 
sales volume at the Texas facility.























                                      9
<PAGE>   10
PART II.  OTHER INFORMATION

ITEM 6:         EXHIBITS AND REPORTS ON FORM 8-K
          --------------------------------
          a.  Exhibits:

              10   International Swap Dealers Association Master
                   Agreement dated as of April 3, 1998 among CoreStates 
                   Bank, N.A. and the Company.

              11   Statement re computation of per share earnings (loss)

              27   Financial Data Schedule

          b.  Reports on Form 8-K:

              The Company filed no Reports on Form 8-K during the
              quarter ended March 31, 1998.








































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<PAGE>   11
                                 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.

                                       UNITED STATES LIME & MINERALS, INC.






April 27, 1998                         By:   \s\  Timothy W. Byrne    
                                           -------------------------
                                            Timothy W. Byrne
                                            President, Chief Executive Officer
                                            and Chief Financial Officer









































                                     11
<PAGE>   12
                     UNITED STATES LIME & MINERALS, INC.



                       Quarterly Report on Form 10-Q
                              Quarter Ended
                              March 31, 1998

                            Index to Exhibits



      Exhibit No.                         Exhibit                           
      -----------       ---------------------------------------------------

          10            International Swap Dealers Association Master
                        Agreement dated as of April 3, 1998 among CoreStates 
                        Bank, N.A. and the Company.

          11            Statement re computation of per share earnings (loss)
 
          27            Financial Data Schedule




































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