<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, 1998              Commission File number 1-5341
                  --------------                                     ------

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


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



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

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



         Indicate by check mark whether the Registrant (1) has filed all reports
required to be filed by Section 13 or 15(d) of the Securities Exchange Act of
1934 during the preceding 12 months (or for such shorter period that the
Registrant was required to file such reports), and (2) has been subject to such
filing requirements for the past 90 days. Yes [X].  No [ ].

         As of close of business on May 4, 1998, Registrant had outstanding
13,288,757 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                                                                            3-31-98           6-30-97
                                                                                ------------      ------------
<S>                                                                             <C>               <C>         
CURRENT ASSETS
Cash and cash equivalents                                                       $      2,823      $      3,601
Trade receivables, less allowance of $736 and $545                                    47,773            43,178
Inventories -
         Finished goods                                                               22,676            26,400
         Work-in-process                                                                 433               441
         Raw materials                                                                11,897             6,586
                                                                                ------------      ------------
                  Total inventories                                                   35,006            33,427
                                                                                ------------      ------------

Prepaid expenses and other                                                             2,816             3,572
Deferred income taxes                                                                  2,296             2,508
                                                                                ------------      ------------
                  Total current assets                                                90,714            86,286
                                                                                ------------      ------------

PROPERTY, PLANT AND EQUIPMENT, AT COST                                               189,172           180,115
         Less - accumulated depreciation                                             (70,718)          (62,648)
                                                                                ------------      ------------
                  Property, plant and equipment, net                                 118,454           117,467
                                                                                ------------      ------------

OTHER ASSETS                                                                           1,749             3,490
                                                                                ------------      ------------
                                                                                $    210,917      $    207,243
                                                                                ============      ============

LIABILITIES AND SHAREHOLDERS' EQUITY
CURRENT LIABILITIES
Accounts payable                                                                $     12,974      $     15,899
Accrued liabilities                                                                   11,695            12,386
                                                                                ------------      ------------
                  Total current liabilities                                           24,669            28,285
                                                                                ------------      ------------

LONG-TERM DEBT                                                                        48,700            52,600
DEFERRED INCOME TAXES                                                                 14,920            13,578

SHAREHOLDERS' EQUITY -
         Common stock                                                                 13,328             8,814
         Paid-in-capital                                                              67,643            71,350
         Retained earnings                                                            42,365            33,039
                                                                                ------------      ------------
                                                                                     123,336           113,203
         Less - Treasury stock, at cost, 27,600 and 17,500 shares at
                  March 31, 1998 and June 30, 1997, respectively                        (708)             (423)
                                                                                ------------      ------------
                  Total shareholders' equity                                         122,628           112,780
                                                                                ------------      ------------
                                                                                $    210,917      $    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                Nine Months Ended
                                                    -----------------------------     -----------------------------
                                                       3-31-98          3-31-97          3-31-98          3-31-97
                                                    ------------     ------------     ------------     ------------
<S>                                                 <C>              <C>              <C>              <C>         
SALES                                               $     59,225     $     57,120     $    193,706     $    172,292
                                                    ------------     ------------     ------------     ------------

COST AND EXPENSES
         Cost of sales                                    45,225           45,347          147,927          135,113
         Selling, general and administrative               8,257            7,609           25,446           23,186
                                                    ------------     ------------     ------------     ------------
INCOME FROM OPERATIONS                                     5,743            4,164           20,333           13,993
                                                    ------------     ------------     ------------     ------------

OTHER EXPENSE
         Interest expense, net                               514               34            1,887              247
                                                    ------------     ------------     ------------     ------------

INCOME BEFORE INCOME TAXES                                 5,229            4,130           18,446           13,746
         Provision for income taxes                        1,860            1,518            6,735            5,057
                                                    ------------     ------------     ------------     ------------
NET INCOME                                          $      3,369     $      2,612     $     11,711     $      8,689
                                                    ============     ============     ============     ============


INCOME PER COMMON SHARE
            - BASIC                                 $        .25     $        .20     $        .88     $        .66
                                                    ============     ============     ============     ============
            - DILUTED                               $        .25     $        .20     $        .87     $        .65
                                                    ============     ============     ============     ============

DIVIDENDS PER COMMON SHARE                          $        .06     $        .05     $        .18     $        .14
                                                    ============     ============     ============     ============

AVERAGE COMMON SHARES
OUTSTANDING - BASIC                                       13,269           13,202           13,234           13,170
                                                    ============     ============     ============     ============
            - DILUTED                                     13,544           13,362           13,504           13,272
                                                    ============     ============     ============     ============
</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
                                                                                                 --------------------------
                                                                                                  3-31-98          3-31-97
                                                                                                 ----------      ----------
<S>                                                                                              <C>             <C>       
CASH FLOWS FROM OPERATING ACTIVITIES

         Net income                                                                              $   11,711      $    8,689
         Adjustments to reconcile net income
            to net cash from operating activities:

                  Depreciation and amortization                                                       8,116           5,937
                  Deferred income taxes                                                               1,554           3,761
                  Changes in assets and liabilities:
                     Trade receivables                                                               (4,595)           (987)
                     Inventories                                                                     (1,579)          2,722
                     Prepaid expenses and other                                                         756          (1,774)
                     Accounts payable and accrued liabilities                                        (3,616)         (1,921)
                                                                                                 ----------      ----------

         Net cash provided by operating activities                                                   12,347          16,427
                                                                                                 ----------      ----------

CASH FLOWS FROM INVESTING ACTIVITIES

         Additions to property, plant and equipment                                                  (9,079)        (13,490)
         Other                                                                                        1,718             856
                                                                                                 ----------      ----------

         Net cash used for investing activities                                                      (7,361)        (12,634)
                                                                                                 ----------      ----------

CASH FLOWS FROM FINANCING ACTIVITIES

         Long-term borrowings, net                                                                   (3,900)         (3,100)
         Dividends on common stock                                                                   (2,385)         (1,846)
         Treasury stock transactions and other, net                                                     521             211
                                                                                                 ----------      ----------

         Net cash used for financing activities                                                      (5,764)         (4,735)
                                                                                                 ----------      ----------

NET DECREASE IN CASH AND CASH EQUIVALENTS                                                              (778)           (942)

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

CASH AND CASH EQUIVALENTS AT END OF PERIOD                                                       $    2,823      $    2,802
                                                                                                 ==========      ==========
</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 representation of the
         results of operations for the three-month and nine-month periods ending
         March 31, 1998 and 1997, but are, however, subject to year-end audit by
         the company's independent auditors. Because of seasonal,
         weather-related conditions in some of the company's market areas, sales
         can vary at times, and results of any one quarter or other interim
         reporting period should not necessarily be considered as indicative of
         results for a full fiscal year.

2.       Effective December 15, 1997, the company increased its unsecured
         revolving credit facility from $80 million to $100 million and the term
         was extended to December 15, 2002. There were no changes to the
         financial covenants or to the interest rate the company currently pays
         for either LIBOR based borrowings or prime rate based borrowings.
         However, the commitment fee for the average unused portion of the line
         was reduced from .25% to .175%.

3.       In September 1997, the Board of Directors declared a three-for-two
         stock split payable in the form of a stock dividend which was
         distributed on November 12, 1997. An amount equal to the par value of
         the common shares issued in connection with the split was transferred
         from paid-in capital to the common stock account. Appropriate
         references to number of shares and to per share information in the
         Consolidated Financial Statements have been adjusted to reflect the
         stock split on a retroactive basis.




                                        5

<PAGE>   6

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

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



<TABLE>
<CAPTION>
                                                                                              (In thousands)
                                                                           Three Months Ended                Nine Months Ended
                                                                        3-31-98          3-31-97          3-31-98          3-31-97
                                                                     ------------     ------------     ------------     ------------
<S>                                                                  <C>              <C>              <C>              <C>         
Net Income                                                           $      3,369     $      2,612     $     11,711     $      8,689
                                                                     ============     ============     ============     ============

Denominator for basic earnings
     per share - weighted average                                          13,269           13,202           13,234           13,170
     shares outstanding

Effect of dilutive securities:
     Employee stock options                                                   275              160              270              102
                                                                     ------------     ------------     ------------     ------------

Denominator for dilutive earnings per share -
adjusted weighted average shares and assumed issuance
of shares purchased under incentive stock option plan
using the treasury stock method                                            13,544           13,362           13,504           13,272
                                                                     ============     ============     ============     ============

Basic earnings per share                                             $        .25     $        .20     $        .88     $        .66
                                                                     ============     ============     ============     ============

Diluted earnings per share                                           $        .25     $        .20     $        .87     $        .65
                                                                     ============     ============     ============     ============
</TABLE>




                                        6

<PAGE>   7

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, 1998 COMPARED TO THE THREE
MONTH PERIOD ENDED MARCH 31, 1997.

During the three month period ended March 31, 1998, net income increased 29% to
$3,369,000 from $2,612,000 in the same quarter last year. Sales increased 4%
compared to the prior year quarter. The increase in sales was primarily related
to continuing strong demand in the Industrial Products Group. The increase in 
net income was achieved by improved performance and higher operating profit in 
both the Roofing Products Group and the Industrial Products Group.

The Roofing Products Group achieved slightly higher sales with increased
operating profit for the three months ended March 31, 1998 compared to the same
prior year period. Although Elk Corporation's shipments of premium laminated
fiberglass asphalt shingles were marginally higher in the current year quarter
as compared to the same three month period in the prior year, shipments in the
current year were limited by El Nino's impact on the West Coast and in the
Southeastern United States, as many roofing contractors were not able to replace
leaking roofs during the extended periods of heavy rainfall. Elk's roofing mat
operations achieved significantly higher sales and much improved operating
profit during the quarter ended March 31, 1998 as a result of growing demand for
its high quality roofing mats and specialty industrial products.

Elcor's Roofing Products segment continues to experience growing demand for its
Elk subsidiary's patented Enhanced High Definition(R) and Raised Profile(TM)
Prestique premium laminated fiberglass asphalt shingles. El Nino's punishing
high winds and heavy rainfall across much of the nation this winter is expected
to significantly increase the level of demand for Elk Prestique laminated
shingles during the seasonally stronger June and September quarters.
Accordingly, Elk has begun implementing a series of small price increases in
each of its markets. In addition, Elk anticipates sharply higher demand from a
broader customer base for its nonwoven fiberglass roofing mats during the
seasonally stronger period.

The Industrial Products Group again recorded significantly higher sales and
operating profit during the three months ended March 31, 1998 as compared to the
same period in the prior year. Chromium Corporation continued to benefit from
strong demand for its Compushield(R) conductive coatings and conductive gaskets
used in wireless digital telecommunications and other electronic equipment
industries. Chromium also experienced higher sales and significantly improved
margins in plating certain proprietary finishes for large diesel engine
components during the three months ended March 31, 1998 as compared to the same
three month period last year.

On an overall basis, gross margin on sales was 23.6% for the quarter ended March
31, 1998 compared to 20.6% in the prior year quarter. The improvement in margin
was primarily attributable to higher margins received for mat products and for
the company's products in the Industrial Products Group. Selling, general and
administrative costs were 13.9% of sales in the current year quarter compared to
13.3% of sales in the prior year quarter. Interest expense was significantly
higher in the third quarter of fiscal 1998 compared to the same quarter in the
prior fiscal year. During the previous year, most interest cost was capitalized
in connection with the company's major facilities expansion program, which was
completed in March 1997.




                                        7

<PAGE>   8




CHANGES IN THE NINE MONTH PERIOD ENDED MARCH 31, 1998, AS COMPARED TO THE NINE
MONTH PERIOD ENDED MARCH 31, 1997.

During the nine month period ended March 31, 1998, net income increased 35% to
$11,711,000 from $8,689,000 in the same period last year. Sales increased 12%
compared to the comparable prior year period. The increases in sales and net
income were primarily attributable to increased shipments of premium roofing
mats, together with much higher sales and income contribution by the Industrial
Products Group during the nine month period ended March 31, 1998.

In the Roofing Products Group, both sales and operating income were higher for
the nine months ended March 31, 1998 as compared to the same period in the prior
fiscal year. The western United States, which is served by the Shafter,
California roofing plant, produced very strong demand for Elk Prestique premium
laminated shingles. Elk's other roofing plants also continued to be very
profitable in the first nine months of fiscal 1998. Sales and operating income
from Elk's mat operations were much higher in the first nine months of fiscal
1998 compared to the same period in fiscal 1997 as a result of increasing demand
for products and improved operating efficiencies at the new Ennis, Texas
facility, which achieved its performance test level of operations effective
April 1, 1997.

The Industrial Products Group achieved sharply higher sales and operating income
in the nine month period ending March 31, 1998 compared to the same prior year
period. Increased demand and improved results were achieved in each of the
Group's principal operations of (1) conductive coatings used in wireless digital
telecommunications and electronic equipment industries; (2) remanufactured
diesel engine components used in the transportation industry; and (3) technology
licensing and consulting services for the natural gas processing industry.

On an overall basis, for the first nine months of fiscal 1998, gross margin on
sales was 23.6%, compared to 21.6% for the same period in the prior fiscal year.
This increase is primarily attributable to higher sales with better margins in
the Industrial Products Group. Higher selling, general and administrative costs
are primarily the result of increased business activity in the current year. As
a percentage of sales, such expenses were 13.1% of sales for the first nine
months of fiscal 1998, down from 13.5% of sales for the same period in the prior
fiscal year. Higher interest expense in the current year is the result of
capitalization of most interest cost in the prior year in connection with the
company's major facilities expansion program.

FINANCIAL CONDITION

Total invested capital at March 31, 1998 was $171,328,000. Long-term debt of
$48,700,000 represented 28% of total capitalization. At March 31, 1998,
$49,710,000 was available under the company's unsecured revolving line of
credit, which was increased to $100 million on December 15, 1997 so as to
provide additional financial resources to support the company's growth
strategies.

Cash provided by operations for the nine months ended March 31, 1998 was
$12,347,000. The current ratio was 3.7 to 1 at March 31, 1998. Working capital
increased $8,044,000 from June 30, 1997, primarily related to a seasonal
increase in trade receivables and inventories, partially offset by lower
accounts payable. 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. In addition, 



                                        8

<PAGE>   9
receivables generally increase during the late winter and early spring months
due to extended payment terms to certain customers during these months with
payment generally due during the summer months. Further, in March 1998, the
company accelerated its raw material purchases of fiberglass fibers prior to the
implementation of announced price increases.

The company utilized $5,764,000 of cash for financing activities in the first
nine months of fiscal 1998, primarily for repayment of long-term debt and
payment of dividends on common stock. The company used $7,361,000 for net
investing activities in the first nine months of fiscal 1998. Capital
expenditures for fiscal 1998 are expected to be in the range of $12,000,000 to
$15,000,000. The majority of planned capital expenditures are for productivity,
capacity, and cost improvement projects at the current roofing plants and for
the development of new computer systems. 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
applied to plastic enclosures for wireless digital telecommunications and
electronic equipment.

In September 1997, the Board of Directors increased the regular quarterly cash
dividend to six cents per common share (after giving effect to a stock split)
and declared a three-for-two stock split payable in the form of a stock dividend
which was 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 March 31, 1998, 248,350
shares (after giving effect to the stock split) with a cumulative cost of
$3,390,000 had been purchased 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.




                                        9

<PAGE>   10
NEW ACCOUNTING PRONOUNCEMENT

In April 1998, the Accounting Standards Executive Committee (AcSEC) of the
American Institute of Certified Public Accountants issued Statement of Position
98-5, "Reporting on the Costs of Start-Up Activities," requiring, among other
things, companies to expense on a current basis previously capitalized start-up
costs. At March 31, 1998, the company had $7,255,000 of unamortized capitalized
start-up costs. This Statement of Position is effective for financial
statements for fiscal years beginning after December 15, 1998, unless adopted
earlier. The company has not yet determined when this new accounting
pronouncement will be adopted.

YEAR 2000 ISSUE

The company is currently developing a new information system for its critical
financial, distribution and manufacturing applications. This system is scheduled
for completion and full implementation in the summer of 1999 at an estimated
total cost of about $8 million. While the primary purpose of this new
information system is to modernize and improve the company's operations, it is
also expected to resolve the Year 2000 issues in these critical computer
systems.

The company also has teams of employees and consultants who are reviewing other
computer applications and systems not included in the scope of the new
information system, and its interaction with its suppliers, customers and other
business partners for Year 2000 readiness. The company is in the process of
taking relevant inventory, assessing risk, assigning priorities to various tasks
and performing limited internal tests. It expects to have fully developed action
and contingency plans by the end of calendar 1998 and for integrated testing and
any remediation to be complete before January 1, 2000. At this time, other than
the cost of developing and implementing its new information system, the company
does not believe that the costs of addressing the Year 2000 issue will be
material, nor will this issue result in uncertainty that is reasonably likely to
affect future financial results or operating performance. Furthermore, the
company believes its Year 2000 readiness project is on schedule for timely
completion.

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 somewhat cyclical
                  and is affected by weather and some of the economic factors
                  that affect the housing and home improvements 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.




                                       10

<PAGE>   11




     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 for 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.

     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 judgements in making investment
            decisions.





                                       11

<PAGE>   12
PART II.  OTHER INFORMATION

ITEM 1:   Legal Proceedings

GAF Patent Litigation

In the ongoing patent litigation with GAF, on April 17, 1998, the district court
entered a partial final judgement in the design patent case based on its
inequitable conduct ruling and certified the case for appeal. Elk is in the
process of filing a notice of appeal with the district court. Elk expects its
appeal to be decided by the United States Court of Appeals for the Federal
Circuit in 1999. In the interim, trial on the trade dress claim and certain
other matters in the design patent case and trial in the utility patent case are
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

On May 8, 1998, plaintiffs in the Daniels case filed a notice of partial
non-suit with the district court in Dallas, pursuant to which Chromium and other
generator defendants were non-suited from the case, without prejudice. Pre-trial
proceedings in the Adams case and appeal from the decision dismissing Chromium
and other generator defendants from the Williams case still are pending.

For further information and background on the above matters and other legal
proceedings, see "Part I, Item 3. Legal Proceedings" in the Registrant's Annual
Report on Form 10-K for the year ended June 30, 1997, and "Part II, Item 1.
Legal Proceedings" in its Quarterly Report on Form 10-Q for the quarter ended
September 30, 1997.


 ITEM 6:         Exhibits and Reports of Form 8-K

       (a)       Exhibits:

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

       (b)       The registrant filed one report on Form 8-K during the quarter
                 ended March 31, 1998. The registrant filed a Form 8-K on
                 January 20, 1998 relating to a press release containing
                 "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, 1998                   /s/ Richard J. Rosebery
     ---------------------               -------------------------------------
                                         Richard J. Rosebery
                                         Vice Chairman, Chief Financial &
                                         Administrative Officer and Treasurer



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



                                       13
<PAGE>   14

                               INDEX TO EXHIBITS


<TABLE>
EXHIBIT
NUMBER              DESCRIPTION
------              -----------
<S>                 <C>
27                  FINANCIAL DATA SCHEDULE
</TABLE>