<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, 1996               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)
  
       

            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 4, 1996, Registrant had
outstanding 8,775,301 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                                                                               9-30-96        6-30-96
------                                                                               -------        -------
<S>                                                                               <C>              <C>
CURRENT ASSETS
Cash and cash equivalents                                                         $    2,775       $    3,744
Trade receivables, less allowance of $490 and $477                                    47,301           42,482
Inventories -
         Finished goods                                                               13,040           20,512
         Work-in-process                                                                 761              604
         Raw materials                                                                 5,678            5,632
                                                                                  ----------       ----------
                Total inventories                                                     19,479           26,748
                                                                                  ----------       ----------

Prepaid expenses and other                                                               946            1,956
Deferred income taxes                                                                  2,691            2,734
                                                                                  ----------       ----------
                Total current assets                                                  73,192           77,664
                                                                                  ----------       -----------

PROPERTY, PLANT AND EQUIPMENT, AT COST                                               172,250          163,053
        Less - accumulated depreciation                                              (54,352)         (52,846)
                                                                                  ----------       ---------- 
                Property, plant and equipment, net                                   117,898          110,207
                                                                                  ----------       ----------

NET ASSETS OF DISCONTINUED OPERATIONS                                                  2,988            2,942
OTHER ASSETS                                                                           1,301            1,315
                                                                                  ----------       ----------
                                                                                  $  195,379       $  192,128
                                                                                  ==========       ==========
LIABILITIES AND SHAREHOLDERS' EQUITY
------------------------------------
CURRENT LIABILITIES
Accounts payable                                                                  $   14,730       $   15,503
Accrued liabilities                                                                   14,414           13,091
                                                                                  ----------       ----------
                Total current liabilities                                             29,144           28,594
                                                                                  ----------       ----------

LONG-TERM DEBT                                                                        51,900           53,000
DEFERRED INCOME TAXES                                                                  9,172            8,336

SHAREHOLDERS' EQUITY -
         Common stock                                                                  8,802            8,802
         Paid-in-capital                                                              71,244           71,555
         Retained earnings                                                            25,653           22,499
                                                                                  ----------       ----------
                                                                                     105,699          102,856
         Less - Treasury stock, at cost, 29,875 and 33,949 shares                       (536)            (658)
                                                                                  ----------       ----------
                Total shareholders' equity                                           105,163          102,198
                                                                                  ----------       ----------
                                                                                  $  195,379       $  192,128
                                                                                  ==========       ==========


</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
                                                                                  -------------------------
                                                                                   9-30-96         9-30-95
                                                                                   -------         -------

<S>                                                                               <C>              <C>
SALES                                                                             $  64,536        $ 48,528
                                                                                  ---------        --------
COST AND EXPENSES
        Cost of sales                                                                50,524          35,856
        Selling, general and administrative                                           7,897           6,752
                                                                                  ---------        --------  
INCOME FROM OPERATIONS                                                                6,115           5,920
                                                                                  ---------        --------
OTHER EXPENSE
        Interest expense, net                                                           161              25
                                                                                  ---------        --------
INCOME BEFORE INCOME TAXES                                                            5,954           5,895
        Provision for income taxes                                                    2,186           2,232
                                                                                  ---------        --------
NET INCOME                                                                        $   3,768        $  3,663
                                                                                  =========        ========


INCOME PER COMMON AND COMMON EQUIVALENT SHARE                                     $     .43        $    .41
                                                                                  =========        ========
DIVIDENDS PER COMMON SHARE                                                        $     .07        $    .06
                                                                                  =========        ========

AVERAGE COMMON AND COMMON EQUIVALENT SHARES
  OUTSTANDING                                                                         8,793           8,843
                                                                                  =========        ========
</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
                                                                                -----------------------
                                                                                9-30-96         9-30-95
                                                                                --------       --------
<S>                                                                            <C>             <C>
CASH FLOWS FROM OPERATING ACTIVITIES

     Net income                                                                 $  3,768       $  3,663
     Adjustments to reconcile net income
         to net cash from operating activities:

              Depreciation and amortization                                        1,915            775
              Deferred income taxes                                                  879            857
              Changes in assets and liabilities:
                Trade receivables                                                 (4,819)         1,237
                Inventories                                                        7,269           (126)
                Prepaid expenses and other                                         1,010          1,164
                Accounts payable and accrued liabilities                             550            573
                                                                                --------       --------

     Net cash provided by operating activities                                    10,572          8,143
                                                                                --------       --------  

CASH FLOWS FROM INVESTING ACTIVITIES

     Additions to property, plant & equipment                                     (9,599)        (8,066)
     Other                                                                           (39)           (14)
                                                                                --------       --------   
     Net cash provided by (used for) investing
     activities                                                                   (9,638)        (8,080)
                                                                                --------       --------   
                                                                               
CASH FLOWS FROM FINANCING ACTIVITIES

     Long-term borrowings, net                                                    (1,100)        (1,200)
     Dividends on common stock                                                      (614)          (524)
     Treasury stock transactions and other, net                                     (189)           (56)
                                                                                --------       -------- 

     Net cash provided by (used for) financing
     activities                                                                   (1,903)        (1,780)
                                                                                --------       -------- 

NET INCREASE (DECREASE) IN CASH AND CASH EQUIVALENTS                                (969)        (1,717)
                                                                                                         

CASH AND CASH EQUIVALENTS AT BEGINNING OF YEAR                                     3,744          3,731
                                                                                --------       --------

CASH AND CASH EQUIVALENTS AT END OF PERIOD                                      $  2,775       $  2,014
                                                                                ========       ========


</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 1996 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, 1996 and 1995, 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.

3.    Effective October 31, 1996, the Company increased its unsecured revolving
      credit facility from $70 million to $80 million, the term was extended 
      by one year to October 31, 1999, and certain financial covenants were 
      adjusted. There were no changes to the interest rate the Company 
      currently pays for either LIBOR based borrowings or prime rate based 
      borrowings.


                                      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, 1996, net income increased to
$3,768,000 from $3,663,000 in last year's first quarter.  Sales increased 33%
compared to the prior year first quarter.  Sales for the first quarter of
fiscal 1997 were significantly higher and net income improved compared to last
year's first quarter, primarily as a result of increased production and
shipments of the Company's patented Enhanced High Definition(R) and Raised
Profile(TM) Prestique(R) premium laminated fiberglass asphalt shingles.  A
significant part of the increased shipments were from the new roofing plant at
Shafter, California.  The ability of this new plant to better serve customers
in the Western United States has permitted the Company to expand its sales and
marketing efforts to better serve customers in the Midwestern and Northeastern
United States with products from its other roofing plants.  Overall gross
margin, as a percentage of sales, was 21.7% during the quarter ended September
30, 1996 compared to 26.1% during the same prior year quarter.  This reduction
in gross margin is primarily attributable to an operating loss of about
$1,300,000 at the new Shafter, California plant during the quarter.  Certain
planned changes were being made to the new plant's production line towards the
end of the first quarter which are expected to enhance the plant's overall
performance in subsequent periods.

Selling, general and administrative (S,G&A) expenses increased 17% during the
first quarter of fiscal 1997 compared to the same prior year quarter.  However,
S,G&A costs were only 12% of sales in the current year quarter compared to 14%
of sales in the prior year quarter.  The Company has established a larger sales
organization to better serve growing market areas.  This larger organization
has been able to service the significant increase in sales orders without a
proportionate increase in overall selling costs.

Start-up operations at the Company's new nonwoven fiberglass mat plant at
Ennis, Texas were underway during the first quarter.  During the quarter ended
September 30, 1996, about $1,700,000 of deferred preoperating costs at the new
Ennis facility were included in capital expenditures.

The Company's industrial products businesses, which account for less than 10%
of consolidated sales and earnings, also reported improved sales and operating
income during the quarter ended September 30, 1996 as compared to the same
prior year quarter.

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 now constitute about 85% of industry
unit sales, are generally less severely affected by economic downturns than
product demand for new residential construction.


                                      6


<PAGE>   7

FINANCIAL CONDITION

The Company's financial condition at September 30, 1996 was very strong.  Total
invested capital  was $157,063,000.  Long-term debt represented 33% of total
capitalization.  At September 30, 1996, $16,100,000 was available under the
Company's $70 million unsecured revolving line of credit.  Effective October
31, 1996, the revolving credit facilities were increased to $80 million to
provide additional financial resources to support the Company's growth
strategies.

Cash generated by operations for the three months ended September 30, 1996 was
$10,572,000. Working capital requirements (excluding cash and cash equivalents)
decreased $4,053,000.  The current ratio was 2.5 to 1 at September 30, 1996.
During the first quarter ended September 30, 1996, the substantial increase in
sales resulted in a $7,269,000 decrease in inventory, partially offset by a
$4,819,000 increase in trade receivables.  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 $9,638,000 for investing activities in the first quarter of
fiscal 1997.  The majority of these investments were for capital expenditures
and related deferred preoperating expenses incurred in connection with the new
nonwoven fiberglass mat plant at the Ennis, Texas facility, which was in
start-up during the quarter ended September 30, 1996, and  changes in the
production line at the Shafter, California plant to enhance the plant's overall
performance.  Total capital expenditures are expected to be significantly less
in fiscal 1997 than in recent years, which included significant capital
expenditures relating to the construction of the two new major manufacturing
facilities.

The Company utilized $1,903,000 for financing activities in the first quarter
of fiscal 1996, primarily for repayment of long-term debt and dividends on
common stock.

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, 1996,
94,800 shares with a cumulative cost of $1,440,000 had been repurchased under
this program.  In September 1995, the Board of Directors reinstated the
Company's regular quarterly cash dividend.  In September 1996, the Board of
Directors increased the regular quarterly cash dividend by 17% to seven cents
per common share.

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.



                                      7

<PAGE>   8
Management believes that cash and cash equivalents, cash flows from operations
and its revolving credit facility should be sufficient during fiscal 1997 and
beyond to fund its currently projected capital expenditure requirements,
working capital needs, dividends, stock repurchases and other cash
requirements.


OUTLOOK

At the present time, we expect that strong demand for our patented Enhanced
High Definition and Raised Profile Prestique shingles will increase shipments
and sales to record levels for fiscal 1997.  We continue to believe that
earnings per share during the second and third quarters should be in the
general range of, or  possibly lower than, the fiscal 1996 comparable quarters
until the manufacturing output and sales at both new plants rise above the
break-even point.  We expect that fourth quarter earnings will benefit from the
seasonal increase in demand for products produced by these two new major
facilities.  Our current forecast for earnings per share for fiscal year ending
June 30, 1997 remains in the range of $1.30 to $1.50 per share, up from $1.16
per share in fiscal 1996.

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.      The Company has completed a $100 million expansion program
                 which included a new roofing plant in Shafter, California and
                 the construction of a new plant at the Company's Ennis, Texas
                 facility to manufacture nonwoven fiberglass roofing mat and
                 industrial facer products for the construction


                                      8


<PAGE>   9
                 industry.  As new facilities, their 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 either of
                 these 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.

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
        
       A hearing before the District Court for the Northern District of Texas   
       to interpret the claims of Elk's design and utility patents is scheduled
       for December 9, 1996, with trial in the design patent case scheduled for
       April 21, 1997, and trial in the utility patent case yet to be
       scheduled.

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, 1996.


ITEM 6.  Exhibits and Reports of Form 8-K

       (a)       Exhibits
                        

                 Exhibit (4.9):      Third Amendment dated October 31, 1996 
                                     to Loan Agreement dated September 29, 1993
                                     among Elcor Corporation, NationsBank of 
                                     Texas, N.A., as Issuer, Administrative 
                                     Lender, and Lender; and Bank of America - 
                                     Texas, N.A. and Comerica Bank - Texas as 
                                     Lenders.                                  

                 Exhibit (11):       Computation of Income Per Common and 
                                     Common Equivalent Share              
                                     
                 Exhibit (27):       Financial Data Schedule (EDGAR Submission 
                                     only)                                


        (b)     The Registrant filed a Form 8-K on August 20, 1996 relating to
a press release containing "forward-looking statements" about its prospects for
the future.

                                      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, 1996          /s/ Richard J. Rosebery
     -------------------------       ----------------------------------------- 
                                     Richard J. Rosebery  
                                     Executive Vice President,                 
                                     Chief Administrative & Financial Officer,  
                                     and Treasurer                             


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



                                      11




<PAGE>   12
                                EXHIBIT INDEX



    EXHIBIT                                                     
    NUMBER                      DESCRIPTION                     
    -------                     -----------                     
                                                                   
Exhibit (4.9):      Third Amendment dated October 31, 1996     
                    to Loan Agreement dated September 29, 1993 
                    among Elcor Corporation, NationsBank of    
                    Texas, N.A., as Issuer, Administrative     
                    Lender, and Lender; and Bank of America -  
                    Texas, N.A. and Comerica Bank - Texas as   
                    Lenders.                                   
                                                                   
Exhibit (11):       Computation of Income Per Common and       
                    Common Equivalent Share 
                                                                   
Exhibit (27):       Financial Data Schedule (EDGAR Submission  
                    only)                                      




                          
                                      12