<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    March 31, 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 May 5, 1997, Registrant had outstanding
8,791,452 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                                                             3-31-97     6-30-96
                                                                  ---------   ---------
<S>                                                               <C>         <C>      
CURRENT ASSETS
Cash and cash equivalents                                         $   2,802   $   3,744
Trade receivables, less allowance of $526 and $477                   43,469      42,482
Inventories -
         Finished goods                                              16,760      20,512
         Work-in-process                                                801         604
         Raw materials                                                6,465       5,632
                                                                  ---------   ---------
                  Total inventories                                  24,026      26,748
                                                                  ---------   ---------

Prepaid expenses and other                                            3,730       1,956
Deferred income taxes                                                 2,713       2,734
                                                                  ---------   ---------
                  Total current assets                               76,740      77,664
                                                                  ---------   ---------

PROPERTY, PLANT AND EQUIPMENT, AT COST                              177,726     163,053
      Less - accumulated depreciation                               (59,945)    (52,846)
                                                                  ---------   ---------
                  Property, plant and equipment, net                117,781     110,207
                                                                  ---------   ---------

NET ASSETS OF DISCONTINUED OPERATIONS                                 2,052       2,942
OTHER ASSETS                                                          1,328       1,315
                                                                  ---------   ---------
                                                                  $ 197,901   $ 192,128
                                                                  =========   =========
LIABILITIES AND SHAREHOLDERS' EQUITY
CURRENT LIABILITIES
Accounts payable                                                  $  14,545   $  15,503
Accrued liabilities                                                  12,128      13,091
                                                                  ---------   ---------
                  Total current liabilities                          26,673      28,594
                                                                  ---------   ---------

LONG-TERM DEBT                                                       49,900      53,000
DEFERRED INCOME TAXES                                                12,076       8,336

SHAREHOLDERS' EQUITY -
         Common stock                                                 8,806       8,802
         Paid-in-capital                                             71,315      71,555
         Retained earnings                                           29,342      22,499
                                                                  ---------   ---------
                                                                    109,463     102,856

         Less - Treasury stock, at cost, 9,100 and 33,949 shares       (211)       (658)
                                                                  ---------   ---------
                  Total shareholders' equity                        109,252     102,198
                                                                  ---------   ---------
                                                                  $ 197,901   $ 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   Nine Months Ended
                                           3-31-97   3-31-96   3-31-97  3-31-96
                                           -------  --------  --------  --------
<S>                                        <C>      <C>       <C>       <C>     
SALES                                      $57,120  $ 50,048  $172,292  $143,938
                                           -------  --------  --------  --------

COST AND EXPENSES
      Cost of sales                         45,347    38,875   135,113   108,696
      Selling, general and administrative    7,609     7,312    23,186    21,417
      Reduction in value of assets               0         0         0       558
                                           -------  --------  --------  --------
INCOME FROM OPERATIONS                       4,164     3,861    13,993    13,267
                                           -------  --------  --------  --------

OTHER EXPENSE
      Interest expense, net                     34        61       247       105
                                           -------  --------  --------  --------

INCOME BEFORE INCOME TAXES                   4,130     3,800    13,746    13,162
      Provision for income taxes             1,518     1,479     5,057     5,054
                                           -------  --------  --------  --------
NET INCOME                                 $ 2,612  $  2,321  $  8,689  $  8,108
                                           =======  ========  ========  ========


INCOME PER COMMON AND COMMON EQUIVALENT
SHARE                                      $   .29  $    .26  $    .98  $    .92
                                           =======  ========  ========  ========

DIVIDENDS PER COMMON SHARE                 $   .07  $    .06  $    .21  $    .18
                                           =======  ========  ========  ========

AVERAGE COMMON AND COMMON EQUIVALENT
SHARES OUTSTANDING                           8,908     8,875     8,848     8,852
                                           =======  ========  ========  ========


</TABLE>


See accompanying notes to consolidated financial statements.








                                       3

<PAGE>   4







                               ELCOR CORPORATION
                      CONSOLIDATED STATEMENT OF CASH FLOWS
                          (Unaudited, $ in thousands)
<TABLE>
<CAPTION>
                                                                                 Nine Months Ended
                                                                                  3-31-97   3-31-96
                                                                                 --------   --------
<S>                                                                               <C>        <C>     

CASH FLOWS FROM OPERATING ACTIVITIES

      Net income                                                                  $  8,689   $  8,108
      Adjustments to reconcile net income
         to net cash from operating activities:

               Depreciation and amortization                                         5,937      2,655
               Reduction in value of assets                                              0        558
               Deferred income taxes                                                 3,761      3,751
               Changes in assets and liabilities:
                   Trade receivables                                                  (987)    (6,800)
                   Inventories                                                       2,722    (10,515)
                   Prepaid expenses and other                                       (1,774)       192
                   Accounts payable and accrued liabilities                         (1,921)     4,442
                                                                                  --------   --------

      Net cash provided by operating activities                                     16,427      2,391
                                                                                  --------   --------

CASH FLOWS FROM INVESTING ACTIVITIES

      Additions to property, plant & equipment                                     (13,490)   (33,233)
      Other                                                                            856       (999)
                                                                                  --------   --------

      Net cash provided by (used for) investing activities                         (12,634)   (34,232)
                                                                                  --------   --------

CASH FLOWS FROM FINANCING ACTIVITIES

      Long-term borrowings (reductions), net                                        (3,100)    32,000
      Dividends on common stock                                                     (1,846)    (1,575)
      Treasury stock transactions and other, net                                       211        393
                                                                                  --------   --------

      Net cash provided by (used for) financing activities                          (4,735)    30,818
                                                                                  --------   --------

NET INCREASE (DECREASE) IN CASH AND CASH EQUIVALENTS                                  (942)    (1,023)

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

CASH AND CASH EQUIVALENTS AT END OF PERIOD                                        $  2,802   $  2,708
                                                                                  ========   ========
</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 and nine-month periods ended
         March 31, 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 or other
         interim reporting period 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. The amendment to the credit facility did not
         change 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

CHANGES IN THE THREE-MONTH PERIOD ENDED MARCH 31, 1997 COMPARED TO THE
THREE-MONTH PERIOD ENDED MARCH 31, 1996.

During the three-month period ended March 31, 1997, net income increased to
$2,612,000 from $2,321,000 for the same three-month period last year. Sales
increased 14% compared to the same prior year quarter. Increased growth in
demand for the Company's patented Enhanced High Definition(R) and Raised
Profile(TM) Prestique(R) premium laminated fiberglass asphalt shingles
accounted for most of the increase in sales. The increase in net income was
primarily related to significantly increased sales and income by the Company's
industrial products businesses.

Despite increased shipments of premium laminated fiberglass asphalt shingles,
operating income for the Company's roofing products group was lower, primarily
due to higher freight rates and raw material costs, together with the costs of
implementing a fourth shift operation at Elk Corporation's Tuscaloosa, Alabama
roofing plant to increase its production capacity. Overall gross margin, as a
percentage of sales, was 20.6% during the quarter ended March 31, 1997 compared
to 22.3% during the same prior year quarter. In addition to the higher costs
described above, a large percentage of the increased sales were from the new
Shafter, California roofing plant, which despite significant improvements in
operations and a good contribution to operating income, has higher fixed costs
(primarily depreciation and amortization) that reduce the gross margin
percentage.

Start-up operations at the Company's new nonwoven fiberglass roofing mat plant
at Ennis, Texas were underway during the quarter ended March 31, 1997. This new
plant is expected to meet its production performance criteria in the fourth
quarter of fiscal 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 now constitute about 82% of industry
unit sales, are generally less severely affected by economic downturns than
product demand for new residential construction.

The Company's industrial products businesses achieved significantly increased
sales and operating income during the quarter ended March 31, 1997 as compared
to the same prior year quarter, primarily as a result of increased fees
generated by Ortloff Engineers, Ltd. from licensing the Company's cryogenic
technology. Several domestic and international patent licenses and technology
agreements were executed during the third quarter, and the outlook appears to
be very good for licensing the Company's process technology for construction of
both new natural gas processing plants and retrofits to upgrade existing gas
processing plants. Additionally, Chromium Corporation achieved higher revenues
relating to its Compushield conductive coatings applied to plastic enclosures
for electronic equipment.

Overall selling, general and administrative (S,G&A) expenses increased 4%
during the quarter ended March 31, 1997 compared to the same prior year
quarter. However, as a percentage of sales, S,G&A costs were 13.3% of sales in
the current year quarter compared to 14.6% of sales in the prior year quarter.

                                       6

<PAGE>   7




CHANGES IN THE NINE-MONTH PERIOD ENDED MARCH 31, 1997, AS COMPARED TO THE
NINE-MONTH PERIOD ENDED MARCH 31, 1996.

During the nine-month period ended March 31, 1997, net income increased to
$8,689,000 from $8,108,000 in the same period last year. Sales increased 20%
compared to the comparable prior year period. The increase in sales was
primarily attributable to increased shipments of premium laminated fiberglass
asphalt shingles during the nine-month period ended March 31, 1997. The
Company's industrial products businesses also achieved significantly higher
revenues in the current year period as compared to the same nine-month period
in the prior fiscal year. The increase in net income is primarily attributable
to increased fees generated from patent licenses and technology agreements
relating to the Company's cryogenic technology for processing of natural gas
and refinery gas streams.

Despite the increase in shipments by the Company's roofing products group,
operating income in this business segment declined in the current fiscal year
as compared to the same prior year period. The Company's new roofing plant at
Shafter, California has made significant progress in operating results since
completion of changes in the production line during the first quarter of fiscal
1997. However, the significant reduction in the operating loss at this plant
achieved in the nine-month period ended March 31, 1997 has been offset by lower
operating profit at the other roofing facilities, primarily in the seasonally
slower quarter ended March 31, 1997 primarily as a result of higher freight
rates, higher raw material costs and costs of implementing a fourth shift
operation at Elk Corporation's Tuscaloosa, Alabama roofing plant to increase
its production capacity.

The Company's industrial products business segment achieved higher sales and
operating income during the nine-month period ended March 31, 1997 compared to
the comparable prior year period, primarily as a result of higher patent
licensing fees and technology agreements by Ortloff Engineers, Ltd.

Overall selling, general and administrative expenses increased 8% during the
first nine months of fiscal 1997 compared to the same prior year period.
However, S,G&A costs were only 13.5% of sales in the current year period
compared to 14.9% of sales in the prior year period. The Company has
established a larger sales organization to better serve growing market areas.
This larger organization has been able to serve the significant increase in
sales orders without a proportionate increase in overall selling costs.

During the nine-month period ended March 31, 1997, approximately $1,450,000 of
deferred start-up costs at the new Ennis facility were capitalized and included
in capital expenditures.

FINANCIAL CONDITION

The Company's financial condition at March 31, 1997 continued to be very
strong. The current ratio was 2.9 to 1 at March 31, 1997. Total invested
capital was $159,152,000. Long-term debt represented 31% of total
capitalization. At March 31, 1997, $28,510,000 was available under the
Company's unsecured revolving line of credit.

Cash generated by operations for the nine months ended March 31, 1997 was
$16,427,000. Working capital requirements (excluding cash and cash equivalents)
increased $1,939,000. The increase in working capital primarily related to a
reduction in current liabilities. However, trade receivables

                                       7

<PAGE>   8




increased $987,000 from June 30, 1996, primarily due to the higher level of
sales and seasonal marketing programs to certain customers that provided
deferred payment terms. The deferred receivables are primarily due in the May
1997 through July 1997 timeframe. Inventory levels at March 31, 1997 were below
the June 30, 1996 levels due to a high level of product shipments in March
1997. Inventory levels are expected to increase during the spring and early
summer months in anticipation of continuing strong demand for the Company's
premium laminated fiberglass asphalt roofing products during the seasonally
stronger period of mid-March through about mid-November. 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 $12,634,000 for investing activities in the first nine months
of fiscal 1997. The majority of these expenditures 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 period ended March 31, 1997, and changes in the
production line at the Shafter, California plant in the early part of fiscal
1997 to enhance the plant's overall performance. Total capital expenditures are
expected to be less in fiscal 1997 than in recent years, which included
significant capital expenditures relating to the construction of the two new
major manufacturing facilities. Capital expenditures are presently expected to
be about $16,000,000 during the current fiscal year.

The Company utilized $4,735,000 for financing activities in the first nine
months of fiscal 1997, primarily as a result of a reduction in long-term debt
and payment of 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 March 31, 1997, 127,900
shares with a cumulative cost of $2,059,000 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 processes. 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 Standards 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 1997 and
beyond to fund its currently projected capital expenditure requirements,
working capital needs, dividends, stock repurchases and other cash
requirements.

                                       8

<PAGE>   9




OUTLOOK

We expect that continuing strong demand for the Company's patented Enhanced
High Definition and Raised Profile Prestique shingles will increase shipments
and sales to record levels for fiscal 1997. In addition, we expect continuing
increases in earnings for the Company's industrial products group during the
fourth quarter of fiscal 1997. At present, we expect that fourth quarter
earnings will be well above last year's level and enable the Company to achieve
its prior forecast calling for fiscal 1997 earnings per share in the range of
$1.30 to $1.50 per share, up from $1.16 per share in fiscal 1996.

FORWARD-LOOKING STATEMENTS

In an effort to give investors a well-rounded view of the Company's current
condition and future opportunities, this Form 10-Q contains "forward-looking
statements" about the Company's prospects for the future. Because they are
forward-looking, 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 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.





                                       9

<PAGE>   10




     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.






                                      10

<PAGE>   11




                           PART II. OTHER INFORMATION



ITEM 1:    Legal Proceedings

GAF Patent Litigation

In December 1996, the District Court for the Northern District of Texas
conducted a hearing to interpret the claims of Elk's design and utility
patents, but has yet to issue a ruling in that matter, which essentially will
determine the scope of the patents. The court also conducted a bench trial on
the inequitable conduct defenses alleged by GAF in the design patent case in
February 1997. A decision in that matter is pending. Trial for the remaining
issues in the design patent case, which was scheduled for April 21. 1997, has
been continued to a date not yet determined, and trial in the utility patent
case has not been scheduled as yet.

Frontier Chemical Site

In February 1997, a court hearing was conducted on the motion for summary
judgement of certain PRP's, including Chromium, in the suit seeking recovery of
$1.2 million of proceeds from a closure bond for the Frontier Chemical Royal
Avenue Site. A ruling on the motion is pending.

In March 1997, the USEPA issued its demand for future costs pursuant to the
Administrative Order on Consent for the Frontier Chemical Royal Avenue Site.
The PRPs have objected to this cost demand and have demanded an accounting.
Resolution of this dispute still is pending, but even if the USEPA demand
remains at the current amount, no further assessments from Chromium will be
necessary to meet it.

Gibraltar Tort Litigation

The court in Daniels recently vacated its June 2, 1997 trial date, and no new
trial date has been set. No trial date has been set in the Williams or Adams
cases. The three Gibraltar cases naming Chromium remain in the early stages.

For information and background on the GAF Patent Litigation, Frontier Chemical
Site, Gibraltar Tact 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, and "Part II, Item 1. Legal
Proceedings" in the Company's Quarterly Report on 10-Q for the quarters ended
September 30, 1996 and December 31, 1996.






                                      11

<PAGE>   12





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 a Form 8-K on January 16, 1997 relating
                  to a press release containing an announcement of quarterly
                  results including "forward-looking statements" about its
                  prospects for the future.


                                      12

<PAGE>   13





                                   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:     May 14, 1997                     /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



                                      13

<PAGE>   14

                                 EXHIBIT INDEX


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

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