<PAGE>   1

                             SECURITIES AND EXCHANGE
                                   COMMISSION

                             Washington, D.C. 20549

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

                                    FORM 10-Q

                   Quarterly Report Under Section 13 or 15(d)
                     of the Securities Exchange Act of 1934

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


For Quarter Ended September 30, 1998               Commission File number 1-5341
                  ------------------                                      ------

                                ELCOR CORPORATION
             ------------------------------------------------------
             (Exact name of Registrant as specified in its charter)


           DELAWARE                                                 75-1217920
-------------------------------                             ------------------
(State or other jurisdiction of                               (I.R.S. Employer
incorporation or organization)                             Identification No.)


            14643 DALLAS PARKWAY
SUITE 1000, WELLINGTON CENTRE, DALLAS, TEXAS                        75240-8871
--------------------------------------------                        ----------
(Address of principal executive offices)                            (Zip Code)

Registrant's telephone number, including area code                (972) 851-0500
                                                                  --------------


         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   .
                                             ---    ---

         As of close of business on November 2, 1998, Registrant had outstanding
12,982,214 shares of Common Stock, Par Value $1 per Share.
<PAGE>   2



PART I.  FINANCIAL INFORMATION

ITEM 1.  Financial Statements

                                ELCOR CORPORATION
                           CONSOLIDATED BALANCE SHEET
                           (Unaudited, $ in thousands)

<TABLE>
<CAPTION>
ASSETS                                                                    9-30-98         6-30-98
------                                                                   ---------       ---------
<S>                                                                      <C>             <C>      
CURRENT ASSETS
Cash and cash equivalents                                                $   3,210       $   5,240
Trade receivables, less allowance of $793 and $580                          65,567          56,450
Inventories -
         Finished goods                                                     15,038          20,549
         Work-in-process                                                       432             446
         Raw materials                                                       7,001           7,827
                                                                         ---------       ---------
                  Total inventories                                         22,471          28,822
                                                                         ---------       ---------

Prepaid expenses and other                                                   1,361           1,789
Deferred income taxes                                                        2,153           2,228
                                                                         ---------       ---------
                  Total current assets                                      94,762          94,529
                                                                         ---------       ---------

PROPERTY, PLANT AND EQUIPMENT, AT COST                                     187,110         194,133
         Less - accumulated depreciation                                   (70,244)        (73,401)
                                                                         ---------       ---------
                  Property, plant and equipment, net                       116,866         120,732
                                                                         ---------       ---------

OTHER ASSETS                                                                 1,909           1,783
                                                                         ---------       ---------
                                                                         $ 213,537       $ 217,044
                                                                         =========       =========
LIABILITIES AND SHAREHOLDERS' EQUITY
------------------------------------

CURRENT LIABILITIES
Accounts payable                                                         $  15,518       $  14,579
Accrued liabilities                                                         16,796          12,628
                                                                         ---------       ---------
                  Total current liabilities                                 32,314          27,207
                                                                         ---------       ---------

LONG-TERM DEBT                                                              43,300          48,000
DEFERRED INCOME TAXES                                                       14,044          15,881

SHAREHOLDERS' EQUITY -
         Common stock                                                       13,326          13,326
         Paid-in-capital                                                    66,979          67,862
         Retained earnings                                                  49,671          47,394
                                                                         ---------       ---------
                                                                           129,976         128,582
         Less  -  Treasury stock (260,823 and 100,423 shares, at cost)      (6,097)         (2,626)
                                                                         ---------       ---------
                  Total shareholders' equity                               123,879         125,956
                                                                         ---------       ---------
                                                                         $ 213,537       $ 217,044
                                                                         =========       =========
</TABLE>

See accompanying notes to consolidated financial statements.


                                       2

<PAGE>   3






                                ELCOR CORPORATION
                      CONSOLIDATED STATEMENT OF OPERATIONS
                           (Unaudited, $ in thousands
                             except per share data)



<TABLE>
<CAPTION>
                                                                              Three Months Ended
                                                                             ----------------------
                                                                              9-30-98       9-30-97
                                                                             --------      --------
<S>                                                                          <C>           <C>     
SALES                                                                        $ 85,868      $ 73,516
                                                                             --------      --------

COST AND EXPENSES
         Cost of sales                                                         63,063        55,401
         Selling, general and administrative                                   10,272         8,805
                                                                             --------      --------
INCOME FROM OPERATIONS                                                         12,533         9,310
                                                                             --------      --------

OTHER EXPENSE
         Interest expense, net                                                    559           759
                                                                             --------      --------

INCOME BEFORE INCOME TAXES                                                     11,974         8,551
         Provision for income taxes                                             4,448         3,157
                                                                             --------      --------
INCOME BEFORE CUMULATIVE EFFECT OF
         CHANGE IN ACCOUNTING PRINCIPLE                                         7,526         5,394

CUMULATIVE EFFECT OF CHANGE IN
         ACCOUNTING PRINCIPLE                                                  (4,340)            0
                                                                             --------      --------

NET INCOME                                                                   $  3,186      $  5,394
                                                                             ========      ========

INCOME PER COMMON SHARE-BASIC:
         Before cumulative effect of change in accounting principle          $    .57      $    .41
         Cumulative effect of change in
           accounting principle                                                  (.33)           --
                                                                             --------      --------
NET INCOME PER SHARE-BASIC                                                   $    .24      $    .41
                                                                             ========      ========

INCOME PER COMMON SHARE-DILUTED:
         Before cumulative effect of change in accounting principle          $    .56      $    .40
         Cumulative effect of change in
          accounting principle                                                   (.32)           --
                                                                             --------      --------
NET INCOME PER SHARE-DILUTED                                                 $    .24      $    .40
                                                                             ========      ========

DIVIDENDS PER COMMON SHARE                                                   $    .07      $    .06
                                                                             ========      ========
</TABLE>

See accompanying notes to consolidated financial statements.


                                                                 3





<PAGE>   4






                                ELCOR CORPORATION
                      CONSOLIDATED STATEMENT OF CASH FLOWS
                           (Unaudited, $ in thousands)


<TABLE>
<CAPTION>
                                                                              Three Months Ended
                                                                              ------------------
                                                                             9-30-98        9-30-97
                                                                             -------        -------

CASH FLOWS FROM OPERATING ACTIVITIES

<S>                                                                         <C>             <C>     
         Net income                                                         $   3,186       $  5,394
         Adjustments to reconcile net income
            to net cash from operating activities:

                  Depreciation and amortization                                 2,230          2,683
                  Deferred income taxes                                           580            773
                  Cumulative effect of change in accounting principle           4,340             --
                  Changes in assets and liabilities:
                     Trade receivables                                         (9,117)        (7,648)
                     Inventories                                                6,351          5,518
                     Prepaid expenses and other                                   428          2,117
                     Accounts payable and accrued liabilities                   5,107            398
                                                                             --------       --------

         Net cash provided by operating activities                             13,105          9,235
                                                                             --------       --------

CASH FLOWS FROM INVESTING ACTIVITIES

         Additions to property, plant and equipment                            (5,037)        (1,791)
         Other                                                                   (134)           (29)
                                                                             --------       --------

         Net cash used for investing activities                                (5,171)        (1,820)
                                                                             --------       --------

CASH FLOWS FROM FINANCING ACTIVITIES

         Long-term borrowings, net                                             (4,700)        (7,100)
         Dividends on common stock                                               (909)          (794)
         Treasury stock transactions and other, net                            (4,355)           120
                                                                             --------       --------

         Net cash used for financing activities                                (9,964)        (7,774)
                                                                             --------       --------

NET DECREASE IN CASH AND CASH EQUIVALENTS                                      (2,030)          (359)

CASH AND CASH EQUIVALENTS AT BEGINNING OF YEAR                                  5,240          3,601
                                                                             --------       --------

CASH AND CASH EQUIVALENTS AT END OF PERIOD                                   $  3,210       $  3,242
                                                                             ========       ========
</TABLE>

See accompanying notes to consolidated financial statements.


                                       4

<PAGE>   5



                                ELCOR CORPORATION
                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS
                                   (Unaudited)



1.       The attached condensed consolidated financial statements have been
         prepared pursuant to the rules and regulations of the Securities and
         Exchange Commission. As a result, certain information and footnote
         disclosures normally included in financial statements prepared in
         accordance with generally accepted accounting principles have been
         condensed or omitted. The company believes that the disclosures
         included herein are adequate to make the information presented not
         misleading. These condensed consolidated financial statements should be
         read in conjunction with the consolidated financial statements and
         related notes included in the company's 1998 Annual Report on Form
         10-K. The unaudited financial information contained herein has been
         prepared in conformity with generally accepted accounting principles on
         a consistent basis and does reflect all adjustments which are, in the
         opinion of management, necessary for a fair presentation of the results
         of operations for the three-month periods ending September 30, 1998 and
         1997, but are, however, subject to year-end audit by the company's
         independent auditors. Because of seasonal, weather-related conditions
         in some of the company's market areas, sales can vary at times, and
         results of any one quarter or other interim reporting period should not
         necessarily be considered as indicative of results for a full fiscal
         year.

2.       In fiscal 1998, the company changed its method of accounting for
         inventories from the LIFO method to the FIFO method. In accordance with
         Accounting Principles Board Opinion No. 20, "Accounting Changes," the
         consolidated financial statements as of September 30, 1997 have been
         restated to reflect this accounting change. There was no significant
         impact on net income for the three months ended September 30, 1997 as a
         result of this change in accounting principle.

3.       In September 1997, the Board of Directors declared a three-for-two
         stock split payable in the form of a stock dividend, which was
         distributed on November 12, 1997. Appropriate references to number of
         shares and to per share information in the consolidated financial
         statements as of September 30, 1997 have been adjusted to reflect the
         stock split on a retroactive basis.

4.       On September 15, 1998, the company experienced an explosion at its
         fiberglass roofing mat plant in Ennis, Texas. The explosion
         significantly damaged a drying oven and caused less extensive damage to
         the remainder of the mat line. At the time of the explosion, the
         damaged mat line supplied all of the company's internal fiberglass
         roofing mat needs. In addition, roofing mats from the damaged line were
         being sold to other asphalt roofing products manufacturers. There was
         no damage to a separate mat line that runs in parallel to the damaged
         line, nor was there any damage to the company's Ennis, Texas shingle
         manufacturing plant. There were no injuries from the explosion.


                                       5

<PAGE>   6



         The company has increased roofing mat production from its nondamaged
         mat line and has begun purchasing additional roofing mats from third
         party suppliers. The company believes there are adequate supplies of
         roofing mats from internal and/or external sources available to operate
         its three roofing shingle manufacturing facilities until the damaged
         line is repaired and fully operational. The company anticipates that
         the damaged line should be restored to partial service by this winter
         and be fully restored by the spring of 1999.

         The company carries both property damage and business interruption
         insurance. Accordingly, management does not expect the explosion to
         have a material adverse impact on the company's financial results. The
         $100,000 deductible portion of the loss was recorded during the quarter
         ended September 30, 1998. 

5.       In the first quarter of fiscal 1999, the company adopted Statement of
         Position 98-5, "Reporting on the Costs of Start-Up Activities," issued
         by the Accounting Standards Executive Committee of the American
         Institute of Certified Public Accountants. This Statement of Position
         requires, among other things, companies to expense on a current basis
         previously capitalized start-up costs. Adoption of this Statement of
         Position resulted in a $4,340,000 charge, net of tax, and is reported
         as a cumulative effect of change in accounting principle on the
         Consolidated Statement of Operations.

6.       During the first quarter of fiscal 1999, the company adopted Statement
         of Financial Accounting Standards No. 130 (SFAS 130), "Reporting
         Comprehensive Income." The adoption of SFAS 130 had no effect on the
         consolidated financial statements, as there are no items that the
         company is required to recognize as components of comprehensive income.

7.       In June 1997, the Financial Accounting Standards Board issued SFAS No.
         131, "Disclosure about Segments of an Enterprise and Related
         Information." SFAS No. 131 requires publicly held companies to
         disclose, among other things, certain interim and annual financial
         information about the enterprise using a new management approach. This
         approach requires segment information to be reported based on how
         management evaluates the operating performance of its business units or
         segments. The company will adopt SFAS No. 131 in fiscal 1999, but is
         still assessing the disclosure requirements of this standard.


                                       6

<PAGE>   7




8.       Basic earnings per share is computed based on the average number of
         common shares outstanding. Diluted earnings per share includes
         outstanding stock options.

         The following table sets forth the computation of basic and diluted
         earnings per share:

<TABLE>
<CAPTION>
                                                    Three Months Ended
                                                   9-30-98      9-30-97
                                                   -------      -------
<S>                                                <C>          <C>    
Net Income                                         $ 3,186      $ 5,394
                                                   =======      =======

Denominator for basic earnings
  per share - weighted average                      13,127       13,202
  shares outstanding

Effect of dilutive securities:
  Employee stock options                               206          242
                                                   -------      -------

Denominator for dilutive earnings
per share - adjusted weighted
average shares and assumed
issuance of shares purchased
under incentive stock option plan
using the treasury stock method                     13,333       13,444
                                                   =======      =======

Basic earnings per share                           $   .24      $   .41
                                                   =======      =======

Diluted earnings per share                         $   .24      $   .40
                                                   =======      =======
</TABLE>

                                       7


<PAGE>   8



ITEM 2. Management's Discussion and Analysis of Financial Condition and Results
of Operations

RESULTS OF OPERATIONS


During the three months ended September 30, 1998, net income before the
cumulative effect of a change in accounting principle increased 40% to
$7,526,000 from $5,394,000 in last year's first quarter. Sales increased 17%
compared to the prior year first quarter. The increases in sales and net income
before the accounting change were primarily the result of increased production
and a record level of shipments of the company's patented Enhanced High
Definition(R) and Raised Profile(TM) Prestique(R) premium laminated fiberglass
asphalt shingles and rapidly accelerating demand for Chromium's Conductive
Coatings Division products used in digital wireless cellular phones. In the
first quarter of fiscal 1999, the company adopted Statement of Position 98-5,
"Reporting on the Costs of Start-Up Activities," issued by the Accounting
Standards Executive Committee of the American Institute of Certified Public
Accountants, which resulted in a $4,340,000 charge, net of tax, for the
cumulative effect of this accounting change. This one-time cumulative charge
reduced net income for the first quarter of fiscal 1999 to $3,186,000 from
$5,394,000, in the same quarter last year.

The Roofing Products Group achieved significantly higher sales with sharply
increased operating profit for the three months ended September 30, 1998
compared to the same prior year period. These increases were primarily the
result of increased manufacturing output and a record level of shipments of
premium laminated fiberglass asphalt shingles. Demand was strong in most
regions of the United States. As a result, each of the company's roofing plants
achieved higher production levels, sales and operating profit in the first
quarter of fiscal 1999 than in the same prior year quarter. The company's
nonwoven fiberglass roofing mat plant also contributed to improved first
quarter results. However, as described in note 4 of this Form 10-Q, this plant
was damaged by an explosion on September 15, 1998. Due to the company's
property damage and business interruption insurance policies, management does
not expect the explosion to have a material adverse impact on the company's
financial results.

The Industrial Products Group recorded both lower sales and lower operating
profit for the first three months of fiscal 1999 compared to the same prior
year period due to lower revenues and income from Ortloff Engineers' technology
licensing and consulting services for the natural gas processing industry.
Lower oil prices have reduced capital spending plans for some of its customers.
Chromium Corporation reported strong growth in sales and operating income,
primarily as a result of accelerating demand for its Compushield conductive
coatings and conductive gaskets used in wireless digital telecommunications and
other electronic equipment industries. Chromium's sales of remanufactured large
diesel engine components also increased in the first quarter of fiscal 1999
compared to the prior year quarter.

On an overall basis, gross margin on sales was 26.6% for the quarter ended
September 30, 1998 compared to 24.6% in the prior year quarter. The improvement
in margin was primarily attributable to increased production, which lowered per
unit costs, at the company's roofing shingle plants. Selling, general and
administrative costs were 12.0% of sales in both the current year quarter and
in the prior year quarter.

At the present time, the company anticipates continued growing demand for its
premium laminated fiberglass asphalt shingles in fiscal 1999, although the
market is seasonally slower in the December and



                                       8
<PAGE>   9


March quarters. Further, the third expansion of its Conductive Coatings facility
is expected to be completed in the second quarter of fiscal 1999. The company
expects the added capacity will be used for increased production of wireless
digital cellular phone components to meet rapidly growing demand for these
products.

FINANCIAL CONDITION

During the first three months of fiscal 1999, the company generated cash flows
of $13,105,000 from operating activities. Of this total, $4,874,000 was the
result of a decrease in working capital. The decrease in working capital was
primarily due to lower cash balances, increased current liabilities and lower
inventories, offset by increased trade receivables. Each of these changes were
primarily the result of increased business activities and higher sales during
the quarter ended September 30, 1998. The current ratio at September 30, 1998
was 2.9:1 compared to 3.5:1 at June 30, 1998. Historically, working capital
requirements fluctuate during the year because of seasonality in some market
areas. Generally, working capital requirements and related borrowings are higher
in the spring and summer months, and lower in the fall and winter months.

The company used $5,171,000 for investing activities in the first three months
of fiscal 1999. The majority of investing expenditures were for additions to
property, plant and equipment. Capital expenditures are expected to be about
$24,000,000 in fiscal 1999 excluding replacement of equipment at the Ennis,
Texas mat plant damaged by an explosion as described in note 4 of this Form
10-Q. The expenditures incurred to replace damaged equipment are expected to be
covered by the company's property damage insurance policy. The majority of
currently planned fiscal 1999 capital expenditures are a continuation of
productivity, capacity and cost improvement projects at its existing roofing
plants, continued capacity expansion of the Conductive Coatings operation, and
capital costs associated with developing new computer systems. The company
expects to invest about $100 million over the next three years to expand
capacity and improve productivity at existing plants and to build new plants in
both the Roofing Products and Industrial Products segments.

Cash flows used for financing activities were $9,964,000 during the first three
months of fiscal 1999, primarily resulting from dividend payments, a $4,700,000
decrease in long-term debt, and purchases of treasury shares. Long-term debt
represented 26% of the $167,179,000 of invested capital (long-term debt plus
shareholders' equity) at September 30, 1998. At September 30, 1998, $54,910,000
was available under the company's $100,000,000 revolving line of credit.

During the first quarter of fiscal 1999, the company purchased 201,200 shares of
its common shares on the open market under SEC Rule 10b-18 at a total cost of
$4,561,000 to complete the $10 million stock buy back program authorized by the
Board of Directors in September 1994. On September 28, 1998, the Board of
Directors authorized an additional $10 million stock repurchase program. The
Board of Directors also increased the regular quarterly cash dividend rate by
17% to $.07 per share effective with the dividend payable November 10, 1998.

The company's operations are subject to extensive federal, state and local laws
and regulations relating to environmental matters. Although the company does not
believe it will be required to expend amounts which will have a material adverse
effect on the company's consolidated financial position or results of operations
by reason of environmental laws and regulations, such laws and regulations are
frequently changed and could result in significantly increased cost of
compliance.



                                       9
<PAGE>   10


Further, certain of the company's industrial products operations utilize
hazardous materials in their production process. As a result, the company incurs
costs for remediation activities off-site and at its facilities from time to
time. The company establishes and maintains reserves for such remediation
activities, when appropriate, in accordance with Statement of Financial
Accounting Standard No. 5, "Accounting for Contingencies." Current reserves
established for known or probable remediation activities are not material to the
company's financial position or results of operations.

Management believes that current cash and cash equivalents, cash flows from
operations and its unsecured revolving credit facility should be sufficient
during fiscal 1999 and beyond to fund its planned capital expenditures, working
capital needs, dividends, stock repurchases and other cash requirements.
However, management believes it could secure additional capital at favorable
rates, if needed, to support its capital expansion program.

YEAR 2000 ISSUE

The company is currently developing a new information system for most of its
critical financial, distribution and manufacturing applications. The system is
scheduled for completion and implementation by the summer of 1999 at an
estimated total cost of about $10 million. While the primary purpose of this new
information system is to modernize and improve the company's operations, it is
also expected to resolve the Year 2000 issues in these critical computer
systems. Costs to develop this new information system are being capitalized.
Other costs relating to Year 2000 readiness are being expensed as incurred. As
of September 30, 1998, the company's expenditures for its new information system
have been $5,016,000, and its expenditures for its Year 2000 readiness projects
have been less than $250,000. At this time, other than the cost of developing
and implementing its new information system, the company does not believe that
the costs of addressing the Year 2000 issue will be material. The company does
not believe that other critical information systems work has been deferred due
to its Year 2000 efforts.

The company also has teams of employees and consultants who are reviewing other
computer applications and systems not included in the scope of the new
information system, including systems other than information systems that have
embedded technology, and its interaction with its suppliers, customers and other
business partners for Year 2000 readiness. The company is close to completing
the process of taking relevant inventory, assessing risk, assigning priorities
to various tasks and performing limited internal tests. The company has
completed its initial remedial programming for its mainframe computer system and
is ready to begin testing this system. The company has developed contingency
plans for its critical information system which primarily consist of making its
existing information system Year 2000 compliant in the event the new system is
not completed by its scheduled date. Contingency plans for other aspects of Year
2000 readiness are currently being developed. The company expects to have fully
developed action plans by the end of calendar 1998, and to have completed
integrated testing and any remediation before January 1, 2000.

The company believes the Year 2000 readiness project is on schedule for timely
completion. Based on a current assessment of risks relating to its Year 2000
readiness, the company does not believe that this issue will result in
uncertainty that is reasonably likely to materially affect future financial
results or operating performance.



                                       10
<PAGE>   11


FORWARD-LOOKING STATEMENTS

This Form 10-Q contains "forward-looking statements" about the company's
prospects for the future. Such statements are subject to certain risks and
uncertainties which could cause actual results to differ materially from those
projected. Such risks and uncertainties include, but are not limited to, the
following:

         1.       The company's roofing products business is cyclical and is
                  affected by weather and some of the same economic factors that
                  affect the housing and home improvement industries generally,
                  including interest rates, the availability of financing and
                  general economic conditions. In addition, the asphalt roofing
                  products manufacturing business is highly competitive. Actions
                  of competitors, including changes in pricing, or slowing
                  demand for asphalt roofing products due to general or industry
                  economic conditions or the amount of inclement weather could
                  result in decreased demand for the company's products, lower
                  prices received or reduced utilization of plant facilities.
                  Further, changes in building codes and other standards from
                  time to time can cause changes in demand, or increases in
                  costs that may not be passed through to customers.

         2.       In the asphalt roofing products business, the significant raw
                  materials are ceramic coated granules, asphalt, glass fibers,
                  resins and mineral filler. Increased costs of raw materials
                  can result in reduced margins, as can higher trucking and rail
                  costs. Historically, the company has been able to pass some of
                  the higher raw material and transportation costs through to
                  the customer. Should the company be unable to recover higher
                  raw material and/or transportation costs from price increases
                  of its products, operating results could be lower than
                  projected.

         3.       During fiscal 1997, the company completed the construction of
                  a plant at the company's Ennis, Texas facility to manufacture
                  nonwoven fiberglass roofing mats and other mats for a variety
                  of industrial uses. The company also expects to make up to
                  $100 million in new investments to expand capacity and improve
                  productivity at existing plants and to build new plants over
                  the next three years. Progress in achieving anticipated
                  operating efficiencies and financial results is difficult to
                  predict for new plant facilities. If such progress is slower
                  than anticipated, if substantial cost overruns occur in
                  building new plants, or if demand for products produced at new
                  plants does not meet current expectations, operating results
                  could be adversely affected.

         4.       Certain facilities of the company's industrial products
                  subsidiaries must utilize hazardous materials in their
                  production process. As a result, the company could incur costs
                  for remediation activities at its facilities or off-site, and
                  other related exposures from time to time in excess of
                  established reserves for such activities.

         5.       The company's litigation, including its patent infringement
                  suits against GAF Building Materials Corporation and certain
                  affiliates, is subject to inherent and case-specific
                  uncertainty. The outcome of such litigation depends on
                  numerous interrelated factors, many of which cannot be
                  predicted.



                                       11
<PAGE>   12



         6.       Even with fully developed action and contingency plans for
                  Year 2000 readiness, it is possible that the company will not
                  achieve full internal readiness. Further, the company's
                  business may be adversely affected by external Year 2000
                  disruption that the company is not in position to control,
                  including but not limited to potential disruptions in power
                  and other energy supplies, telecommunications or other
                  infrastructure, potential disruptions in transportation and
                  the supply of raw materials, and potential disruptions in
                  financial and banking systems. Year 2000 problems therefore
                  could result in unanticipated expenses or liabilities,
                  production or disruption delays or other adverse effects on
                  the company.

         7.       Although the company currently anticipates that most of its
                  needs for new capital in the near future will be met with
                  internally generated funds, significant increases in interest
                  rates could substantially affect its borrowing costs under its
                  existing loan facility, or its cost of alternative sources of
                  capital.

         8.       Each of the company's businesses, especially its Conductive
                  Coatings Division's business, is subject to the risks of
                  technological changes that could affect the demand for or the
                  relative cost of the company's products and services, or the
                  method and profitability of the method of distribution or
                  delivery of such products and services. In addition, the
                  company's businesses each could suffer significant setbacks in
                  revenues and operating income if it lost one or more of its
                  largest customers.

         9.       Although the company insures itself against physical loss to
                  its manufacturing facilities, including business interruption
                  losses, natural or other disasters and accidents, including
                  but not limited to fire, earthquake, damaging winds and
                  explosions, operating results could be adversely affected if
                  any of its manufacturing facilities became inoperable for an
                  extended period of time due to such events.

     Parties are cautioned not to rely on any such forward-looking beliefs or
judgments in making investment decisions.



                                       12
<PAGE>   13


PART II.  OTHER INFORMATION

ITEM 6:   Exhibits and Reports of Form 8-K

       (a)       Exhibit:

                 Exhibit (27):  Financial Data Schedule (EDGAR submission only)

       (b)       The registrant filed two reports on Form 8-K during the quarter
                 ended September 30, 1998. The registrant filed a Form 8-K on
                 August 19, 1998 and a Form 8-K on September 28, 1998, both
                 relating to press releases containing "forward-looking
                 statements" about its prospects for the future.



                                       13
<PAGE>   14


                                   SIGNATURES




Pursuant to the requirements of the Securities and Exchange Act of 1934, the
Registrant has duly caused this report to be signed on its behalf by the
undersigned thereunto duly authorized.



                                      ELCOR CORPORATION



DATE:        November 13, 1998        /s/ Richard J. Rosebery
     --------------------------       --------------------------------------
                                      Richard J. Rosebery
                                      Vice Chairman, Chief Financial &
                                      Administrative Officer and Treasurer

                                      /s/ Leonard R. Harral
                                      --------------------------------------
                                      Leonard R. Harral
                                      Vice President and Chief
                                      Accounting Officer



                                       14
<PAGE>   15


                               INDEX TO EXHIBITS

<TABLE>
<CAPTION>
Exhibit
Number                           Exhibit
-------                          -------
<S>                         <C>
  27                        Financial Data Schedule
</TABLE>