<PAGE>   1


                                                                       CONFORMED
                                  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 SEPTEMBER 30, 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 000-4197




                       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 October 14, 1998,
3,971,165 shares of common stock, $0.10 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>
                                                           SEPTEMBER 30,   DECEMBER 31,
                                                               1998            1997
                                                           -------------   ------------
<S>                                                        <C>             <C>     
ASSETS
Current Assets:
  Cash and cash equivalents                                   $  2,638      $  2,787
  Trade receivables, net                                         3,800         3,624
  Inventories                                                    2,969         3,001
  Prepaid expenses and other assets                                 98           111
                                                              --------      --------
     Total current assets                                        9,505         9,523

Property, plant and equipment at cost                           68,765        52,302
  Less:  Accumulated depreciation and depletion                (31,996)      (30,896)
                                                              --------      --------
  Property, plant and equipment, net                            36,769        21,406

Deferred tax assets, net                                         2,465         2,537
Other assets, net                                                  114            54
                                                              --------      --------

     Total assets                                             $ 48,853      $ 33,520
                                                              ========      ========


LIABILITIES AND STOCKHOLDERS' EQUITY
Current Liabilities:
  Current installments of long-term debt                      $  2,643      $  1,071
  Accounts payable                                               2,648         4,437
  Accrued expenses                                               1,834         1,594
                                                              --------      --------
     Total current liabilities                                   7,125         7,102

Long-term debt, excluding current installments                  15,500         2,167
Other liabilities                                                  253           101
                                                              --------      --------
      Total liabilities                                         22,878         9,370

Stockholders' Equity:
  Common stock                                                     529           529
  Additional paid-in-capital                                    14,930        15,135
  Retained earnings                                             24,554        22,729
                                                              --------      --------
                                                                40,013        38,393
Less treasury stock at cost; 1,322,900 and
  1,342,212 shares of common stock, respectively               (14,038)      (14,243)
                                                              --------      --------
     Total stockholders' equity                                 25,975        24,150
                                                              --------      --------

     Total liabilities and stockholders' equity               $ 48,853      $ 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                        NINE MONTHS ENDED
                                                 SEPTEMBER  30,                           SEPTEMBER  30,
                                      -------------------------------------    --------------------------------------
                                             1998               1997                 1998                  1997
                                      -----------------   -----------------    -----------------    -----------------
<S>                                   <C>         <C>     <C>        <C>       <C>         <C>      <C>         <C>   
REVENUES                              $ 7,423     100.0%  $ 7,725    100.0%    $ 21,908    100.0%   $ 25,883    100.0%

Cost of revenues:
  Labor and other operating expenses    4,902      66.0%    4,537     58.7%      14,582     66.6%     18,929     73.1%
  Depreciation, depletion and
      amortization                        702       9.5%      667      8.7%       2,062      9.4%      2,720     10.5%
                                      -----------------   ----------------     -----------------    -----------------

                                        5,604      75.5%    5,204     67.4%      16,644     76.0%     21,649     83.6%
                                      -----------------   ----------------     -----------------    -----------------


GROSS PROFIT                            1,819      24.5%    2,521     32.6%       5,264     24.0%      4,234     16.4%

  Selling, general and administrative
      expenses                            814      11.0%      878     11.3%       2,657     12.1%      3,148     12.2%
                                      -----------------   ----------------     -----------------    -----------------

OPERATING PROFIT                        1,005      13.5%    1,643     21.3%       2,607     11.9%      1,086      4.2%

  Other deductions (income):
    Interest expense                        6       0.0%       71      0.9%         12      0.0%        372       1.4%
    Other income, net                     (64)     (0.8%)    (206)    (2.6%)      (339)    (1.5%)      (299)     (1.1%)
                                      -----------------   ----------------    -----------------    ------------------

                                          (58)     (0.8%)    (135)     (1.7%)      (327)   (1.5%)        73       0.3%
                                      -----------------   -----------------    ----------------    ------------------


NET INCOME BEFORE
      INCOME TAXES                      1,063      14.3%    1,778      23.0%      2,934     13.4%      1,013      3.9%
                                      -----------------   -----------------    -----------------    -----------------

Federal and state income
      tax expense (benefit)               287       3.9%      457       5.9%        792      3.6%     (1,996)    (7.7%)
                                      -----------------   -----------------    -----------------    -----------------


  NET INCOME                          $   776      10.4%  $ 1,321      17.1%   $  2,142      9.8%   $  3,009     11.6%
                                      =================   =================    =================    =================



INCOME PER SHARE
     OF COMMON STOCK:
          Basic                       $  0.20             $  0.34              $   0.54             $   0.77
                                      =======             =======              ========             ========   

          Diluted                     $  0.20             $  0.33              $   0.54             $   0.76
                                      =======             =======              ========             ========
</TABLE>



    See accompanying notes to condensed consolidated financial statements.


                                       3

<PAGE>   4



UNITED STATES LIME & MINERALS, INC. AND SUBSIDIARIES
CONDENSED CONSOLIDATED STATEMENTS OF CASH FLOWS
(In thousands of dollars)
(Unaudited)

<TABLE>
<CAPTION>
                                                                           NINE MONTHS ENDED
                                                                             SEPTEMBER 30,
                                                                        ----------------------
                                                                          1998          1997
                                                                        --------      --------
<S>                                                                     <C>           <C>     
CASH FLOWS FROM OPERATING ACTIVITIES:
  Net income                                                            $  2,142      $  3,009
  Adjustments to reconcile net income to net cash
        provided by (used in) operating activities:
     Depreciation, depletion and amortization                              2,158         2,831
     Deferred income tax benefit                                              72        (2,220)
     Amortization of financing costs                                          --            50
     Loss on sale of property, plant and equipment                            54            14
     Loss on sale of Corson Lime Company assets                               --           506
     Current assets, net change [1]                                         (131)        1,620
     Other assets                                                            (60)            9
     Current liabilities, net change [2]                                  (1,549)       (1,174)
     Other liabilities                                                       152          (487)
                                                                        --------      --------
     Net cash provided by operating activities                             2,838         4,167

CASH FLOWS FROM INVESTING ACTIVITIES:
  Purchase of property, plant and equipment                              (17,597)       (5,647)
  Proceeds from sale of Corson Lime Company assets, net of expenses           --         7,745
  Proceeds from sale of property, plant and equipment                         22            42
                                                                        --------      --------
     Net cash (used in) provided by investing activities                 (17,575)        2,140

CASH FLOWS FROM FINANCING ACTIVITIES:
  Payment of pension fund liabilities                                        (19)           --
  Proceeds from exercise of stock options                                     --           143
  Payment of common stock dividends                                         (298)         (295)
  Proceeds from borrowings on term loan                                   15,000            --
  Principal payments on term loan debt                                       (95)         (857)
  Proceeds from borrowing on revolving credit facility                        --         2,900
  Principal payments on revolving credit facility                             --        (2,900)
                                                                        --------      --------
     Net cash provided by (used in) financing activities                  14,588        (1,009)
                                                                        --------      --------

  Net increase (decrease) in cash                                           (149)        5,298
     Cash at beginning of period                                           2,787         1,000
                                                                        --------      --------

     Cash at end of period                                              $  2,638      $  6,298
                                                                        ========      ========


  Supplemental cash flow information:
     Interest paid                                                      $    605      $    327
                                                                        ========      ========

     Income taxes paid                                                  $    437      $    451
                                                                        ========      ========


[1] Exclusive of net change in cash
[2] Exclusive of net change in current portion of debt
</TABLE>

    See accompanying notes to condensed consolidated financial statements.

                                       4

<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 three- and nine-month periods ended
     September 30, 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)                               September 30,          December 31,
                                                                      1998                  1997
                                                                 -------------          ------------
         <S>                                                     <C>                    <C> 
              Lime and limestone inventories:
                  Raw materials                                   $      833             $     624
                  Finished goods                                         442                   844
                                                                  ----------             ---------
                                                                       1,275                 1,468
              Service parts                                            1,694                 1,533
                                                                  ----------             ---------
                     Total inventories                            $    2,969             $   3,001
                                                                  ==========             =========
</TABLE>


3.   Long-Term Debt

     The Company has a financing agreement with a commercial bank. The current
     agreement was entered into in August 1998, and amended the amended and
     restated loan agreement which was entered into in December 1997. The prior
     agreement provided for a $15,000,000 five-year secured term loan and a
     $4,000,000 unsecured revolving credit facility which matured in December
     1999. Both loans bore interest at the bank's prime rate but could, at the
     option of the Company, be converted into LIBOR-based loans that bore
     interest at LIBOR plus 1.65% for the term loan and LIBOR plus 1.50% for the
     revolving credit facility. The prior agreement also allowed for 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.

     As part of the prior agreement, the Company negotiated a $25,000,000
     secured line of credit to provide temporary financing for capital
     expenditures and acquisitions until such time as permanent financing could
     be arranged. Any borrowings under this facility would have been at the
     bank's prime rate or, at the discretion of the Company, converted into a
     LIBOR-based loan bearing interest


                                       5

<PAGE>   6


     at LIBOR plus 2%. The capital expenditure and acquisition line of credit
     was available, if not extended, through September 1998 and was subject to
     approval by the bank.


     On August 31, 1998, the Company amended its amended and restated loan
     agreement which was entered into in December 1997. The amendment to the
     agreement provides for an additional $3,500,000, for a total of
     $18,500,000, on the five-year secured term loan. The amended term loan's
     maturity was extended from July 2003 to September 2003 and requires monthly
     principal repayments of $220,238 beginning on October 1, 1998. The amended
     agreement includes a separate secured line of credit of $5,000,000 for
     capital expenditures related to the Arkansas modernization and expansion
     project. This committed capital expenditure line of credit requires
     interest-only payments until its maturity in July 2000. As a result of this
     line of credit, the amended agreement reduced the $25,000,000 capital
     expenditure and acquisition line of credit by $5,000,000 to $20,000,000.
     The amended agreement extended the capital expenditure and acquisition line
     of credit, which remains subject to approval by the bank, through January
     2000 from September 1998. In addition, the amended agreement required the
     $4,000,000 revolving credit facility to be secured and extended its
     maturity to January 2000 from December 1999. All three of the facilities
     are secured by substantially all of the Company's assets and bear interest
     at the bank's prime rate plus a defined interest rate spread based upon the
     Company's then-current ratio of total funded debt to earnings before
     interest, taxes, depreciation and amortization (EBITDA). However, at the
     option of the Company, all or any portion of the amounts outstanding can be
     converted into a LIBOR-based rate plus a defined interest rate spread based
     upon the Company's then-current ratio of total funded debt to EBITDA. The
     term loan and the committed capital expenditure line of credit bear
     interest at LIBOR plus 1.50%, and these rates increase to a maximum of
     LIBOR plus 2.75% if the Company's current ratio of funded debt to EBITDA
     reaches a ratio of 4 to 1. The revolving credit facility bears interest at
     LIBOR plus 1.40%, and its rate increases similar to the other loans based
     on the leverage of the Company.

     A summary of long-term debt is as follows:
<TABLE>
<CAPTION>
         <S>                                                                <C>                   <C> 
         (In thousands of dollars)                                          September 30,        December 31,
                                                                                1998                 1997
                                                                            -------------        -----------
         Term loan                                                           $  18,143              3,238
         Committed capital expenditure line of credit                            -                    -
         Revolving credit facility                                               -                    -
                                                                             ---------           -----------
                  Subtotal                                                      18,143              3,238

         Less current installments                                               2,643              1,071
                                                                             ---------           -----------

         Long-term debt, excluding current installments                      $  15,500               2,167
                                                                             =========           ===========
</TABLE>


     The additional amounts borrowed in the first nine months of 1998 were used
     to partially fund the modernization and expansion project at the Texas
     facility. Interest costs of $285,000 and $590,000 were capitalized as part
     of the Texas project in the three- and nine-month periods ended September
     30, 1998, respectively.

     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 term 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

                                       6

<PAGE>   7


     rates plus 1.65%, 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 term 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.

     For amounts not otherwise fixed under the Swap Agreement, the Company has
     elected the LIBOR-based interest option for the debt outstanding under the
     term loan.

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


                                       7

<PAGE>   8



ITEM 2.  MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL
         CONDITION AND RESULTS OF OPERATIONS


LIQUIDITY AND CAPITAL RESOURCES


Net cash provided by operating activities was $2,838,000 for the nine months
ended September 30, 1998, as compared to $4,167,000 for the nine months ended
September 30, 1997. Excluding the effects of Corson Lime Company in 1997, the
decrease in cash provided by operating activities was primarily attributable to
the reduction of current liabilities from year end.

The Company made $17,597,000 in capital expenditures in the first nine months of
1998, compared to $5,647,000 in the same period last year. Capital expenditures
of approximately $14,763,000 and $1,820,000 were related to the modernization
and expansion project at the Texas facility in the first nine months of 1998 and
1997, respectively. The Texas project includes the installation of new stone
crushing and handling systems, the addition of a preheater to one of the
existing kilns, additional storage, screening and shipping capacity and a new
support building housing a laboratory, administrative offices and shop
facilities.

The Texas project has been constructed in phases and is substantially completed.
The new support building and the stone crushing and handling systems have been
completed. The preheater was added during the months of August and September. In
addition, as of September 30, 1998, one-half of the new storage, screening and
loadout improvements have been made, with the remainder to be completed in the
fourth quarter. The Texas Lime 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 $23,000,000. This project has been
financed through a combination of internally generated funds from operations,
the proceeds from the sale of the Corson Lime Company assets, and the term loan
provided under the Company's banking facilities.

The Company is also moving forward with the modernization and expansion plans at
the Arkansas plant. The Arkansas plans call for construction in two phases. The
first phase, currently scheduled for completion in early 2000, includes the
addition of a new 1,200-ton per day (400,000-ton per year) rotary kiln, new
stone crushing and handling systems, and new lime and ground calcium carbonate
storage and loadout facilities. The second phase of the project, which is
currently scheduled for construction in 2002, but may be accelerated, includes a
rock transportation system and additional lime storage facilities. Permit
applications have been submitted, kiln system design is being finalized, and bid
proposals have been requested for key components of the project. The preliminary
cost estimates for the planned project phases are approximately $27,000,000 and
$5,000,000, respectively. The project is contingent upon satisfactory permitting
from the various regulatory agencies and availability of financing. The Company
has secured a $5,000,000 committed capital expenditure line of credit for the
Arkansas project under its banking facilities, and expects to finance the
remaining costs of 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


                                       8

<PAGE>   9


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
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 September 30, 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 $2,920,000. 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 September 30, 1998, the Company had $18,143,000 in debt outstanding under
its 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.

RESULTS OF OPERATIONS

Revenues decreased from $7,725,000 in the third quarter of 1997 to $7,423,000 in
the third quarter of 1998, a decrease of $302,000, or 3.9%. This resulted from a
3.8% decrease in sales volume and a 0.1% decrease in prices. The decrease in
volume in the third quarter resulted primarily from lower production for
approximately 30 days due to a planned kiln outage at the Texas Lime plant. The
kiln was taken out of production in order to complete the construction of the
preheater. Revenues for the nine months ended September 30, 1998 were
$21,908,000, a decrease of $3,975,000, or 15.4%, from the $25,883,000 reported
for the nine months ended September 30, 1997. Excluding 1997 revenues from
Corson, revenues for the nine months ended September 30, 1998 increased by
$928,000, or 4.4%, from 1997, resulting from a 4.1% increase in sales volume and
a 0.3% increase in prices.

The Company's gross profit was $1,819,000 for the third quarter of 1998,
compared to $2,521,000 for the third quarter of 1997, a 27.9% decrease. Gross
profit margin as a percentage of revenues for the third quarter of 1998
decreased to 24.5% from 32.6% in 1997. Gross profit for the quarter was impacted
by the planned kiln outage at Texas Lime, which resulted in spreading the same
fixed costs over fewer units. In addition, some lime was purchased from
competitors at a loss in order to service existing customers during the
shutdown. Gross profit increased to $5,264,000 for the first nine months of
1998, from $4,234,000 for the first nine months of 1997, a 24.3% increase. Gross
profit margin for the nine months ended September 30, 1998 increased to 24.0%,
from 16.4% in 1997. The 1998 gross profit and gross profit margins were improved
by 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 the first half of 1998 at both the Texas and
Arkansas facilities and the inevitable production inefficiencies in Texas as a
result of the extensive construction activities, including the planned kiln
outage, at that facility. The 1997 gross profit and gross profit margins were
negatively impacted by the loss on the sale of the Corson assets.

Selling, general and administrative expenses ("SG&A") decreased by $64,000, or
7.3%, to $814,000 in the third quarter of 1998, as compared to $878,000 in the
third quarter of 1997. SG&A as a percentage of sales decreased to 11.0% as
compared to 11.3% in the third quarter a year ago. SG&A decreased by $491,000,
or 15.6%, to $2,657,000 in the first nine months of 1998, as compared to
$3,148,000 in the


                                       9


<PAGE>   10

first nine months of 1997, and as a percentage of sales decreased to 12.1% from
12.2% a year earlier. The SG&A expense decrease was primarily attributable to
the shut down of the Corson operations after the sale in June 1997.

Interest expense in the third quarter of 1998 was $6,000 as compared to $71,000
in 1997. Interest expense for the first nine months of 1998 was $12,000 as
compared to $372,000 in 1997. The 1998 decrease was attributable to the
capitalization of substantially all incurred interest costs as part of the Texas
modernization and expansion project. Interest costs of approximately $285,000
and $590,000 were capitalized in the third quarter and first nine months of
1998, respectively.

The Company reported net income of $776,000 ($0.20 per share) during the third
quarter of 1998, compared to net income of $1,321,000 ($0.34 per share) during
the third quarter of 1997. Net income in the third quarter of 1997 was
negatively impacted by the Texas Lime construction project, which affected
production at the plant. For the first nine months of 1998, the Company reported
net income of $2,142,000 ($0.54 per share), compared to net income of $3,009,000
($0.77 per share) in the first nine months of 1997. Net income for the first
nine months of 1997 was favorably impacted by the recognition of previously
reserved deferred tax assets of $2,300,000 ($0.59 per share) and unfavorably
impacted by the loss (net of tax benefit) on the sale of the Corson Lime Company
assets of $405,000 ($0.10 per share) in the second quarter of 1997.

YEAR 2000 COMPLIANCE

The Company has begun addressing the potential impact of the year 2000 ("Y2K")
issue on its operations. The Y2K problem arises because of computer programs
which use two digits rather than four digits to define a year. This may result
in miscalculations or complete system failures in processing data with programs
using date sensitive information.

The Company currently uses certain customized accounting software which is not
Y2K compliant. The Company is in the process of selecting commercially available
accounting software which is scheduled to be installed by the second quarter of
1999. The cost of this installation will be approximately $200,000. Certain
software used in the Company's production operations has either already been
warranted by the suppliers or publishers to be Y2K compliant, or the suppliers
and publishers have represented that such software will be compliant through
upgrades the Company will receive in 1999 under software maintenance agreements.
The Company has not taken any steps to independently verify the truth of such
warranties and representations, but has no reason to believe that the software
is not, or will not be, compliant. Management does not currently believe that
the amount of non-compliant equipment used in other systems will be found to be
significant, nor will the cost to modify or replace such equipment be material.

Management expects to obtain confirmation from its suppliers and customers that
they also are or will be Y2K compliant. The costs of seeking such confirmation
are minimal. Management believes that it will not be practical to independently
verify the responses received because it does not believe that the Company would
be given access to carry out such verification or that the costs of doing so
would be affordable. The cost of replacing, or of implementing alternative means
of communication with, non-compliant or non-responsive suppliers and customers
will not be possible to determine until the review process has been completed.
The Company plans to establish contingency plans, if needed, once its
confirmation program is complete and the risks have been more fully identified
and quantified.

                                       10


<PAGE>   11




PART II. OTHER INFORMATION
ITEM 6:  EXHIBITS AND REPORTS ON FORM 8-K

              a.  Exhibits:

                  10       First Amendment to Amended and Restated Loan Security
                           Agreement, dated August 31, 1998 among United States
                           Lime & Minerals, Inc., Arkansas Lime Company and
                           Texas Lime Company and First Union National Bank

                  11       Statement re computation of per share earnings

                  27       Financial Data Schedule

                  27.1     Restated Financial Data Schedule



              b.  Reports on Form 8-K:

                  The Company filed no Reports on Form 8-K during the quarter
                  ended September 30, 1998.



                                       11

<PAGE>   12




                                   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.



October 14, 1998                     /s/  Timothy W. Byrne
                                     ----------------------------------
                                          Timothy W. Byrne
                                          President, Chief Executive Officer and
                                          Chief Financial Officer


                                       12

<PAGE>   13


                       UNITED STATES LIME & MINERALS, INC.



                          Quarterly Report on Form 10-Q
                                  Quarter Ended
                               September 30, 1998

                                Index to Exhibits



<TABLE>
<CAPTION>
Exhibit No.                                   Exhibit
-----------                     -----------------------------------------
<S>                             <C>                                        
   10                           First Amendment to Amended and Restated Loan
                                Security Agreement, dated August 31, 1998
                                among United States Lime & Minerals, Inc.,
                                Arkansas Lime Company and Texas Lime Company
                                and First Union National Bank

   11                           Statement re computation of per share earnings

   27                           Financial Data Schedule

   27.1                         Restated Financial Data Schedule
</TABLE>