<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, 1997          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 3, 1997, Registrant had outstanding
8,819,166 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                                                                           9-30-97      6-30-97
------                                                                           -------      -------
<S>                                                                             <C>          <C>
CURRENT ASSETS
Cash and cash equivalents                                                       $   3,242    $   3,601  
Trade receivables, less allowance of $711 and $545                                 50,826       43,178  
Inventories -                                                                                           
         Finished goods                                                            21,607       26,400  
         Work-in-process                                                              364          441  
         Raw materials                                                              5,938        6,586  
                                                                                ---------    ---------  
                  Total inventories                                                27,909       33,427  
                                                                                ---------    ---------  
                                                                                                        
Prepaid expenses and other                                                          1,455        3,572  
Deferred income taxes                                                               2,433        2,508  
                                                                                ---------    ---------  
                  Total current assets                                             85,865       86,286  
                                                                                ---------    ---------  
                                                                                                        
PROPERTY, PLANT AND EQUIPMENT, AT COST                                            181,906      180,115  
         Less - accumulated depreciation                                          (65,324)     (62,648) 
                                                                                ---------    ---------  
                  Property, plant and equipment, net                              116,582      117,467  
                                                                                ---------    ---------  
                                                                                                        
OTHER ASSETS                                                                        3,512        3,490  
                                                                                ---------    ---------  
                                                                                $ 205,959    $ 207,243  
                                                                                =========    =========  
LIABILITIES AND SHAREHOLDERS' EQUITY                                                                    
------------------------------------
CURRENT LIABILITIES                                                                                     
Accounts payable                                                                $  13,965    $  15,899  
Accrued liabilities                                                                14,718       12,386  
                                                                                ---------    ---------  
                  Total current liabilities                                        28,683       28,285  
                                                                                ---------    ---------  
                                                                                                        
LONG-TERM DEBT                                                                     45,500       52,600  
DEFERRED INCOME TAXES                                                              14,276       13,578  
                                                                                                        
SHAREHOLDERS' EQUITY -                                                                                  
         Common stock                                                               8,817        8,814  
         Paid-in-capital                                                           71,044       71,350  
         Retained earnings                                                         37,639       33,039  
                                                                                ---------    ---------  
                                                                                  117,500      113,203  
         Less - Treasury stock, at cost, 17,500 shares at June 30, 1997                --         (423) 
                                                                                ---------    ---------  
                                                                                                        
                  Total shareholders' equity                                      117,500      112,780  
                                                                                ---------    ---------  
                                                                                $ 205,959    $ 207,243  
                                                                                =========    =========  

</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
                                               ------------------
                                                9-30-97   9-30-96
                                                -------   -------
<S>                                             <C>       <C>    
SALES                                           $73,516   $64,536
                                                -------   -------

COST AND EXPENSES
        Cost of sales                            55,401    50,524
        Selling, general and administrative       8,805     7,897
                                                -------   -------
INCOME FROM OPERATIONS                            9,310     6,115
                                                -------   -------

OTHER EXPENSE
        Interest expense, net                       759       161
                                                -------   -------

INCOME BEFORE INCOME TAXES                        8,551     5,954
       Provision for income taxes                 3,157     2,186
                                                -------   -------
NET INCOME                                      $ 5,394   $ 3,768
                                                =======   =======


INCOME PER COMMON AND COMMON EQUIVALENT SHARE   $   .60   $   .43
                                                =======   =======

DIVIDENDS PER COMMON SHARE                      $   .09   $   .07
                                                =======   =======

AVERAGE COMMON AND COMMON EQUIVALENT SHARES
  OUTSTANDING                                     8,963     8,793
                                                =======   =======

</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
                                                                ------------------
                                                              9-30-97        9-30-96
                                                              -------        -------
<S>                                                           <C>           <C>     
CASH FLOWS FROM OPERATING ACTIVITIES

      Net income                                              $  5,394      $  3,768
      Adjustments to reconcile net income
         to net cash from operating activities:

               Depreciation and amortization                     2,683         1,915
               Deferred income taxes                               773           879
               Changes in assets and liabilities:
                 Trade receivables                              (7,648)       (4,819)
                 Inventories                                     5,518         7,269
                 Prepaid expenses and other                      2,117         1,010
                 Accounts payable and accrued liabilities          398           550
                                                              --------      --------

      Net cash provided by operating activities                  9,235        10,572
                                                              --------      --------

CASH FLOWS FROM INVESTING ACTIVITIES

      Additions to property, plant & equipment                  (1,791)       (9,599)
      Other                                                        (29)          (39)
                                                              --------      --------

      Net cash used for investing activities                    (1,820)       (9,638)
                                                              --------      --------

CASH FLOWS FROM FINANCING ACTIVITIES

     Long-term borrowings, net                                  (7,100)       (1,100)
     Dividends on common stock                                    (794)         (614)
     Treasury stock transactions and other, net                    120          (189)
                                                              --------      --------

     Net cash used for financing activities                     (7,774)       (1,903)
                                                              --------      --------

NET DECREASE IN CASH AND CASH EQUIVALENTS                         (359)         (969)

CASH AND CASH EQUIVALENTS AT BEGINNING OF YEAR                   3,601         3,744
                                                              --------      --------

CASH AND CASH EQUIVALENTS AT END OF PERIOD                    $  3,242      $  2,775
                                                              ========      ========

</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 1997
     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 ended September 30, 1997
     and 1996, 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 should not necessarily be considered as indicative of
     results for a full fiscal year.

2.   Net income per common and common equivalent share is computed based on the
     average number of common and common equivalent shares outstanding. Common
     equivalent shares include outstanding stock options. There is no material
     difference between primary and fully diluted earnings per share.






                                        5

<PAGE>   6




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

RESULTS OF OPERATIONS

During the first quarter ended September 30, 1997, net income increased 43% to
$5,394,000 from $3,768,000 in last year's first quarter. Sales increased 14%
compared to the prior year first quarter. The increases in sales and net income
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, together
with much higher sales and income contribution by the Industrial Products Group.
A significant part of the increased shipments were in the western United States.
Homeowners' concerns in California that severe El Nino conditions could cause
rain damage from leaking roofs resulted in a strong increase in demand for Elk
Prestique premium laminated shingles. The Industrial Products Group achieved
sharply higher sales and operating profit, sparked by strong demand for Chromium
Corporation's Compushield(R) conductive coatings used in the telecommunications
and electronic equipment industries. In addition, increased demand for
remanufactured diesel engine components used in the transportation industry, and
increased use of Ortloff Engineers' technology licensing and consulting services
for the natural gas processing industry also contributed to improved results.


The overall increase in gross margin on sales to 24.6% for the quarter ended
September 30, 1997 from 21.7% in the prior year quarter is primarily
attributable to higher sales with better margins in the Industrial Products
Group. Selling, general and administrative (S,G&A) expenses increased 11% during
the first quarter of fiscal 1998 compared to the same prior year quarter.
However, S,G&A costs remained at 12% of sales in the current year quarter, the
same as in the prior year quarter. Interest expense was significantly higher in
the first quarter of fiscal 1998 as compared to the same quarter in the prior
fiscal year. During the previous year quarter, most interest costs were
capitalized in connection with the company's major facilities expansion program,
which was completed in March 1997.

The company's roofing products business is cyclical and is affected by some of
the same economic factors that affect the housing industry generally, including
interest rates, the availability of financing and general economic conditions.
However, reroofing and remodeling, which constitutes about 80% of industry unit
sales, are generally less severely affected by economic downturns than product
demand for new residential construction.

FINANCIAL CONDITION

Total invested capital at September 30, 1997 was $163,000,000. Long-term debt of
$45,500,000 represented 28% of total capitalization. At September 30, 1997,
$32,910,000 was available under the company's $80 million unsecured revolving
line of credit. However, the company plans to increase its unsecured revolving
credit facility to a total of $100 million to assure funding of its potential
capital expenditure needs for future growth opportunities.






                                       6

<PAGE>   7


Cash provided by operations for the three months ended September 30, 1997 was
$9,235,000. The current ratio was 3.0 to 1 at September 30, 1997. During the
first quarter ended September 30, 1997, increased sales, especially during the
month of September 1997, resulted in a $7,648,000 increase in receivables, which
was partially offset by a $5,518,000 decrease in inventories. 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 utilized $7,774,000 for financing activities in the first quarter of
fiscal 1998, primarily for repayment of long-term debt and dividends on common
stock. The company used $1,820,000 for investing activities in the first quarter
of fiscal 1998. Capital expenditures for fiscal 1998 are now expected to be in
the range of $12,000,000 to $15,000,000. The majority of currently planned
capital expenditures are for productivity, capacity, and cost improvement
projects at the current roofing plants. In addition, the company is expanding
its capacity in the Chromium Corporation Conductive Coatings Division to meet
rapidly growing demand for its Compushield process for conductive coatings of
plastic enclosures for electronic equipment.

In September 1997, the Board of Directors increased the regular quarterly cash
dividend to nine cents per common share (before giving effect to a stock split)
and declared a three-for-two stock split payable in the form of a stock dividend
to be distributed on November 12, 1997 to shareholders of record at the close of
business on October 16, 1997.

In September 1994, the company's Board of Directors authorized the purchase of
up to $10 million of the company's common shares from time to time on the open
market to be used for general corporate purposes. As of September 30, 1997,
136,300 shares with a cumulative cost of $2,271,000 had been repurchased under
this program.

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.

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 cash and cash equivalents, cash flows from operations
and its revolving credit facility should be sufficient during fiscal 1998 and
beyond to fund its currently projected capital expenditure requirements, working
capital needs, dividends, stock repurchases and other cash requirements.





                                        7

<PAGE>   8


PENDING ACCOUNTING PRONOUNCEMENT

The Accounting Standards Executive Committee (AcSEC) of the American Institute
of Certified Public Accountants has issued an exposure draft on "Reporting on
the Costs of Start-Up Activities." If the exposure draft were to be finalized in
its proposed form, it would require companies to expense on a current basis
previously capitalized start-up costs. At September 30, 1997, the company had
$8,399,000 of unamortized capitalized start-up costs. While the company does not
agree with the accounting treatment proposed in the AcSEC exposure draft and
believes that capitalizing costs incurred in constructing major new facilities
provides a better matching of revenues and expenses, the company will adopt this
statement of position if and when it is finalized.

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.

     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 transportation costs from
          price increases of its products, operating results could be lower than
          projected.

     3.   During fiscal 1997, the company completed construction of a new plant
          at the company's Ennis, Texas facility to manufacture nonwoven
          fiberglass roofing mats and other mats for a variety of industrial
          uses. As a new facility, its progress in achieving anticipated
          operating efficiencies and financial results is difficult to predict.
          If such progress is slower than anticipated, or if demand for products
          produced at this new plant does not meet expectations, operating
          results could be adversely affected.




                                        8

<PAGE>   9


     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.

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






                                       9

<PAGE>   10


                           PART II. OTHER INFORMATION


ITEM 1:   Legal Proceedings

GAF Patent Litigation

In the ongoing patent litigation with GAF, the district court made two
significant rulings. The first concerned the coverage of Elk of Dallas's design
and utility patents and was generally favorable. The second concerned GAF's
inequitable conduct defenses and was unfavorable. Although the court found that
the issue was close, it concluded that the design patent was unenforceable due
to inadequate disclosure to the patent examiner of certain prior art.

Elk of Dallas and its outside counsel disagree strongly with the ruling of
inequitable conduct and will appeal from the ruling at an appropriate time. In
the interim, trial on the trade dress claim in the case and trial in the utility
patent case is unscheduled but pending.

While management can give no assurances regarding the ultimate outcome of the
litigation, outside counsel believe that Elk of Dallas will prevail on its
patent and trade dress claims and that Elk of Dallas will defeat GAF's
counterclaims. Even if the outcome were to be adverse to Elk of Dallas, it is
not expected to have a material effect on the Registrant's financial position or
liquidity.

Gibraltar Tort Litigation

The court in the Daniels case has vacated the October 27, 1997 trial date
without resetting it. A hearing in that case on the Generator Defendants' motion
for summary judgement is scheduled for November 18, 1997.

For further information and background on the GAF Patent Litigation and other
legal proceedings involving the company, see "Part I, Item 3. Legal Proceedings"
in the company's Annual Report on Form 10-K for the year ended June 30, 1997.

ITEM 6:   Exhibits and Reports of Form 8-K

     (a)  Exhibits:

          Exhibit (11): Computation of Income Per Common and Common Equivalent
                        Share

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

     (b) The Registrant filed two reports on Form 8-K during the quarter ended
September 30, 1997. The Registrant filed a Form 8-K on August 19, 1997 relating
to a press release containing "forward-looking statements" about its prospects
for the future. The Registrant also filed a Form 8-K on August 27, 1997 relating
to the death of Roy E. Campbell, the company's Chairman, President and Chief
Executive Officer and the subsequent election by the Board of Directors of
Harold K. Work as the new Chairman, President and Chief Executive Officer.


                                       10

<PAGE>   11


                                   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 12, 1997               /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


                                       11

<PAGE>   12

                                 EXHIBIT INDEX

<TABLE>
<CAPTION>

EXHIBIT
NUMBER                        DESCRIPTION
-------                       -----------
<S>                       <C>                                              
    Exhibit (11):       Computation of Income Per Common and Common Equivalent
                        Share

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

</TABLE>