<PAGE>   1
 
================================================================================
 
                UNITED STATES SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549
 
                            ------------------------
 
                                   FORM 10-Q
 
(Mark One)
 
[X] QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES EXCHANGE
    ACT OF 1934
 
For the quarterly period ended April 3, 1998
 
                                       OR
 
[ ] TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES EXCHANGE
    ACT OF 1934
 
        FOR THE TRANSITION PERIOD FROM                TO
 
                         COMMISSION FILE NUMBER 1-7006
 
                               BRUSH WELLMAN INC.
               (EXACT NAME OF REGISTRANT AS SPECIFIED IN CHARTER)
 
<TABLE>
<S>                                                           <C>
                            OHIO                                           34-0119320
      (STATE OR OTHER JURISDICTION OF INCORPORATION OR        (I.R.S. EMPLOYER IDENTIFICATION NO.)
                       ORGANIZATION)
 17876 ST. CLAIR AVENUE, CLEVELAND,         44110
                OHIO
    (ADDRESS OF PRINCIPAL EXECUTIVE      (ZIP CODE)
              OFFICES)
</TABLE>
 
                                  216-486-4200
               REGISTRANT'S TELEPHONE NUMBER, INCLUDING AREA CODE
 
     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 May 8, 1998 there were 16,557,962 shares of Common Stock, par value
$1 per share, outstanding.
 
================================================================================
<PAGE>   2
 
                         PART I   FINANCIAL INFORMATION
 
                      BRUSH WELLMAN INC. AND SUBSIDIARIES
 
ITEM 1.   FINANCIAL STATEMENTS
 
     The consolidated financial statements of Brush Wellman Inc. and its
subsidiaries for the quarter ended April 3, 1998 are as follows:
 
          Consolidated Statements of Income -- Three months ended April 3, 1998
     and March 28, 1997
 
          Consolidated Balance Sheets -- April 3, 1998 and December 31, 1997
 
          Consolidated Statements of Cash Flows -- Three months ended April 3,
     1998 and March 28, 1997
 
                                        1
<PAGE>   3
 
CONSOLIDATED STATEMENTS OF INCOME
 
(UNAUDITED)
 
<TABLE>
<CAPTION>
                                                                 FIRST QUARTER ENDED
                                                              -------------------------
                                                               APRIL 3,      MARCH 28,
 (DOLLARS IN THOUSANDS EXCEPT SHARE AND PER SHARE AMOUNTS)       1998          1997
---------------------------------------------------------------------------------------
<S>                                                           <C>           <C>
Net sales...................................................  $   114,182   $    99,688
  Cost of sales.............................................       86,153        73,997
                                                              -----------   -----------
Gross Profit................................................       28,029        25,691
  Selling, administrative and general expenses..............       16,334        15,399
  Research and development expenses.........................        2,205         1,578
  Other-net.................................................          696          (522)
                                                              -----------   -----------
Operating Profit............................................        8,794         9,236
  Interest expense..........................................          236           284
                                                              -----------   -----------
Income before income taxes..................................        8,558         8,952
  Income taxes..............................................        2,396         2,462
                                                              -----------   -----------
Net Income..................................................  $     6,162   $     6,490
                                                              ===========   ===========
Per Share of Common Stock: Basic............................  $      0.38   $      0.40
 
Weighted average number of common shares outstanding........   16,317,518    16,165,728
 
Per Share of Common Stock: Diluted..........................  $      0.37   $      0.40
 
Weighted average number of common shares outstanding........   16,715,622    16,274,157
</TABLE>
 
See notes to consolidated financial statements.
                                        2
<PAGE>   4
 
CONSOLIDATED BALANCE SHEETS
 
(UNAUDITED)
 
<TABLE>
<CAPTION>
                                                              APR. 3,     DEC. 31,
(DOLLARS IN THOUSANDS)                                          1998        1997
----------------------------------------------------------------------------------
<S>                                                           <C>         <C>
ASSETS
Current Assets
  Cash and cash equivalents.................................  $    989    $  7,170
  Accounts receivable.......................................    70,494      62,812
  Inventories...............................................    90,516      90,714
  Prepaid expenses and other current assets.................    17,714      18,215
                                                              --------    --------
     Total Current Assets...................................   179,713     178,911
 
Other Assets................................................    31,033      31,319
Property, Plant and Equipment...............................   475,211     463,689
  Less allowances for depreciation, depletion and
     impairment.............................................   295,914     290,067
                                                              --------    --------
                                                              $390,043    $383,852
                                                              ========    ========
LIABILITIES AND SHAREHOLDERS' EQUITY
Current Liabilities
  Short-term debt...........................................  $ 34,710    $ 28,877
  Accounts payable..........................................    10,588      13,519
  Other liabilities and accrued items.......................    25,824      28,580
  Dividends payable.........................................                 1,967
  Income taxes..............................................     8,273       5,369
                                                              --------    --------
     Total Current Liabilities..............................    79,395      78,312
Other Long-Term Liabilities.................................     8,032       8,200
Retirement and Post-Employment Benefits.....................    39,121      39,825
Long-Term Debt..............................................    17,905      17,905
Deferred Income Taxes.......................................     2,853       2,797
Shareholders' Equity........................................   242,737     236,813
                                                              --------    --------
                                                              $390,043    $383,852
                                                              ========    ========
</TABLE>
 
See notes to consolidated financial statements.
                                        3
<PAGE>   5
 
CONSOLIDATED STATEMENTS OF CASH FLOWS
 
(UNAUDITED)
 
<TABLE>
<CAPTION>
                                                                THREE MONTHS ENDED
                                                              ----------------------
                                                              APRIL 3,     MARCH 28,
(DOLLARS IN THOUSANDS)                                          1998         1997
------------------------------------------------------------------------------------
<S>                                                           <C>          <C>
NET INCOME..................................................  $  6,162     $  6,490
ADJUSTMENTS TO RECONCILE NET INCOME TO NET CASH PROVIDED
  FROM OPERATING ACTIVITIES:
  Depreciation, depletion and amortization..................     5,598        4,814
  Amortization of mine development..........................       541            1
  Decrease (Increase) in accounts receivable................    (8,234)     (10,809)
  Decrease (Increase) in Inventory..........................      (157)       2,040
  Decrease (Increase) in prepaid and other current assets...       396         (630)
  Increase (Decrease) in accounts payable and accrued
     expenses...............................................    (5,424)        (547)
  Increase (Decrease) in interest and taxes payable.........     2,855        2,832
  Increase (Decrease) in deferred income tax................        48           33
  Increase (Decrease) in other long-term liabilities........      (822)       1,591
  Other -- net..............................................       381          273
                                                              --------     --------
     NET CASH PROVIDED FROM OPERATING ACTIVITIES............     1,344        6,088
CASH FLOWS FROM INVESTING ACTIVITIES:
  Payments for purchase of property, plant and equipment....   (11,627)     (10,240)
  Payments for mine development.............................      (198)      (2,932)
  Proceeds from (Payments for) other investments............       128          227
                                                              --------     --------
     NET CASH PROVIDED FROM (USED IN) INVESTING
      ACTIVITIES............................................   (11,697)     (12,945)
CASH FLOWS FROM FINANCING ACTIVITIES:
  Proceeds from issuance of short-term debt.................     6,240          316
  Repayment of short-term debt..............................                   (742)
  Repayment of long-term debt...............................                   (160)
  Issuance of Common Stock under stock option plans.........     2,721           93
  Purchase of Common Stock for treasury.....................      (816)        (333)
  Payments of dividends.....................................    (3,930)      (3,573)
                                                              --------     --------
     NET CASH PROVIDED FROM (USED IN) FINANCING
      ACTIVITIES............................................     4,215       (4,399)
 
Effects of Exchange Rate Changes............................       (43)         (63)
                                                              --------     --------
     NET CHANGE IN CASH AND CASH EQUIVALENTS................    (6,181)     (11,319)
     CASH AND CASH EQUIVALENTS AT BEGINNING OF PERIOD.......     7,170       31,749
                                                              --------     --------
  CASH AND CASH EQUIVALENTS AT END OF PERIOD................  $    989     $ 20,430
                                                              ========     ========
</TABLE>
 
See notes to consolidated financial statements.
                                        4
<PAGE>   6
 
NOTES TO CONSOLIDATED FINANCIAL STATEMENTS
 
(UNAUDITED)
 
APRIL 3, 1998
 
NOTE A -- ACCOUNTING POLICIES
 
     In management's opinion, the accompanying consolidated financial statements
contain all adjustments necessary to present fairly the financial position as of
April 3, 1998 and December 31, 1997 and the results of operations for the three
months ended April 3, 1998 and March 28, 1997.
 
NOTE B -- INVENTORIES
 
<TABLE>
<CAPTION>
                                                              APRIL 3,    DEC. 31,
                   (DOLLARS IN THOUSANDS)                       1998        1997
----------------------------------------------------------------------------------
<S>                                                           <C>         <C>
Principally average cost:
  Raw materials and supplies................................  $ 18,209    $ 17,331
  In Process................................................    57,370      58,666
  Finished..................................................    36,798      37,008
                                                              --------    --------
                                                               112,377     113,005
Excess of average cost over LIFO
     inventory value........................................    21,861      22,291
                                                              --------    --------
                                                              $ 90,516    $ 90,714
                                                              ========    ========
</TABLE>
 
NOTE C -- COMPREHENSIVE INCOME
 
     As of January 1, 1998, the Company adopted Statement 130, "Reporting
Comprehensive Income". Statement 130 establishes new rules for the reporting and
display of comprehensive income and its components; however, the adoption of
this statement had no impact on the Company's net income or shareholders'
equity. Statement 130 requires certain items, including foreign currency
translation adjustments, which prior to adoption were reported separately in
shareholders' equity to be included in other comprehensive income. Prior year
financial statements have been reclassified to conform to the requirements of
Statement 130.
 
     During the first quarter 1998 and 1997, comprehensive income amounted to
$5,762,069 and $5,508,288. The difference between net income and comprehensive
income is is the cumulative translation adjustment for the periods presented.
 
NOTE D -- COMPUTER SOFTWARE DEVELOPMENT COSTS
 
     In March 1998, the AICPA issued SOP 98-1, "Accounting For the Costs of
Computer Software Developed For or Obtained For Internal-Use". The SOP is
effective for the Company beginning on January 1, 1999. The SOP will require the
capitalization of certain costs incurred after the date of adoption in
connection with developing or obtaining software for internal-use. The Company
currently expenses such costs as incurred. The Company has not yet assessed what
the impact of the SOP will be on the Company's future earnings or financial
position.
 
                                        5
<PAGE>   7
 
ITEM 2. MANAGEMENT'S DISCUSSION AND ANALYSIS
 
FORWARD-LOOKING INFORMATION
 
     Portions of narrative set forth in this document that are not historical in
nature are forward-looking statements. The Company's actual future performance
may differ from that contemplated by the forward-looking statements as a result
of a variety of factors that include, in addition to those mentioned elsewhere
herein, the condition of the markets which the Company serves, the success of
the Company's strategic plans, the timely and successful completion of pending
capital expansions and the conclusion of pending litigation matters in
accordance with the Company's expectation that there will be no materially
adverse effects.
 
RESULTS OF OPERATIONS
 
     Sales in the first quarter 1998 were $114.2 million, a 14.5% improvement
over first quarter 1997 and an all-time sales record. Revenues from both the
Metal Systems Group and the Microelectronics Group were higher, but overall
earnings declined slightly.
 
     The Metal Systems Group, which consists of strip and bulk alloy products,
engineered material systems and beryllium products, accounted for approximately
75% of total sales and a higher proportion of total profits. Sales of these
products increased dramatically in both the domestic and international markets
in the first quarter 1998 from the first quarter 1997.
 
     Bulk alloy products -- plate, bar, rod and tube -- had the largest sales
improvement. These products are sold into the aerospace, mold, oil and gas and
undersea communication markets. Sales of non-beryllium containing alloys
manufactured at the recently constructed facility in Lorain, Ohio, contributed
to this growth. Sales of precision strip alloy products, which are primarily
copper beryllium alloys and typically used in the telecommunications, automotive
and computer markets, also grew. Low copper prices during the first quarter
1998, as compared to the first quarter 1997, reduced alloy products reported
revenues, but had a minimal impact on profits.
 
     Engineered material systems continued a solid trend of higher sales and
profits in 1998. Telecommunications, automotive and semiconductors are the major
markets served and additional capital is being invested to increase capacity and
manufacturing capabilities.
 
     Beryllium product sales increased as well in the first quarter 1998 over
the prior year. These sales were profitable in 1998 after operating at a loss in
the first quarter 1997.
 
     Microelectronic Group sales, which include precious metals, ceramics and
etched circuits, grew modestly in the first quarter 1998 over first quarter
1997. Precious metal sales increased despite a planned substitution of silver
for gold in certain applications, and the value added from these sales actually
improved at a higher rate than the sales growth. The Company continues to invest
in new products for physical vapor deposition as well as other specialty metal
applications.
 
     Ceramics revenues were higher in 1998 than 1997. However, the resulting
profitability declined dramatically due primarily to yield and performance
issues with the production of direct bond copper products. The implementation of
new production processes has been delayed to the second quarter 1998.
 
     Sales of etched circuits, which account for a minor portion of total sales,
declined slightly in the current period.
 
     The dollar strengthened relative to the yen and German mark in the current
period as compared to first quarter last year. As a result, the translated value
of sales from international operations was reduced, as were margins, since the
majority of the production costs is incurred in dollars. International markets
served are essentially the same as the domestic markets.
 
     Gross margin was $28.0 million, or 24.5% of sales, in the first quarter
1998 compared to $25.7 million, or 25.8% of sales, in the first quarter 1997.
The adverse currency effect and the direct bond copper production
 
                                        6
<PAGE>   8
 
problems were major contributors to the decline in the margin percentage. The
overall product mix was favorable and prices, in general, were firm.
 
     The new casting facility in Elmore, Ohio, part of the three-year $117
million expansion project, began producing high quality beryllium copper alloy
billets in the first quarter 1998. Initial start-up expenses, including training
and additional material testing, negatively impacted margins in the first
quarter 1998. The new facility provides much needed additional capacity and
helps to relieve a portion of the bottlenecks in the manufacturing of strip and
bulk alloy products. The strip mill portion of the project is scheduled to be
completed later in 1998. The total construction cost remains within budget and
is being financed in part by two operating leases. Lease payments for the new
building began in December 1997 while the payments for leasing selected pieces
of equipment do not begin until 1999.
 
     Selling, administrative and general expenses were $16.3 million or 14.3% of
sales in the first quarter 1998 compared to $15.4 million or 15.4% of sales in
the first quarter 1997. Higher employment costs, an increase in workers'
compensation expenses and year 2000 system compliance costs account for the
difference.
 
     Research and development (R&D) expenses of $2.2 million in the first
quarter 1998 were $0.6 million higher than the comparable period in 1997. R&D
activities were planned to increase in order to support new product development
and manufacturing process improvements. Billings for R&D services rendered under
government contracts were less in 1998 than 1997, as a portion of the contract
activity in the first quarter 1998 will not be invoiced until the second quarter
1998.
 
     Other-net expense was $0.7 million in the first quarter 1998 compared to
other net income of $0.5 million in the first quarter 1997. Interest income was
lower in 1998 as a result of the decline in cash balances. Foreign currency
hedge gains were also lower in 1998 than 1997. The precious metal lease fee was
higher in the first quarter 1998 than the first quarter 1997, but lower than the
peak levels from the latter part of 1997 as a result of actions taken by the
Company and stabilization of the available market rates.
 
     Interest expense was $0.2 million in the first quarter 1998 and $0.3
million in the first quarter 1997. These figures are net of capitalized interest
of $0.3 million in both periods. The weighted average interest rate was slightly
less in the first quarter 1998 than in the first quarter 1997.
 
     First quarter 1998 income before income taxes was $8.6 million, a decrease
of 4% from the first quarter last year as higher expense levels, the stronger
dollar, additional direct bond copper manufacturing costs and the new casting
facility start-up costs offset the additional margins generated by the increase
in sales. Income taxes were provided for at 28.0% in the first quarter 1998 and
27.5% in the first quarter 1997. Comparative basic earnings per share are $0.38
in the first quarter 1998 and $0.40 in the first quarter 1997. Diluted earnings
per share for the respective periods are $0.37 and $0.40.
 
FINANCIAL CONDITION
 
     Net cash provided from operations was $1.3 million in the first quarter
1998 compared to $6.1 million in the first quarter 1997. Payments charged
against accounts payable and other accrued items for the 1997 employee
performance awards, the accrued dividend for the fourth quarter 1997 and other
items reduced cash from operating activities in the first quarter 1998. Accounts
receivable increased in the first quarter 1998 primarily due to higher sales
than in the fourth quarter 1997. Inventories were relatively flat in the first
quarter 1998 and turnover improved.
 
     Capital expenditures totaled $11.6 million in the first quarter 1998. Major
expenditures included a portion of the alloy expansion project, the ongoing
implementation of a new information system and new plating lines and mills at
the Lincoln, Rhode Island facility. Capital expenditures were $10.2 million in
the first quarter 1997 while an additional $2.9 million was expended for
developing a new mine that was completed in 1997.
 
     Dividends paid on Common Stock were $3.9 million in the first quarter 1998
and $3.6 million in the first quarter 1997.
 
     Cash balances stood at $1.0 million at the end of the first quarter 1998
compared to $7.2 million at the beginning of the quarter. Total balance sheet
debt increased to $52.6 million from $46.8 million during the
                                        7
<PAGE>   9
 
current quarter. The majority of short-term debt is denominated in precious
metals and foreign currencies. Long-term debt, excluding the off-balance sheet
obligations, was 7% of total capital at the end of the first quarter 1988.
 
     Funds being generated from operations, plus the available borrowing
capacity, are believed adequate to support operating requirements, capital
expenditures, remediation projects, dividends and small acquisitions. Excess
cash, if any, is invested in money market instruments and other high quality
investments.
 
                                        8
<PAGE>   10
 
PART II   OTHER INFORMATION
 
ITEM 1.   LEGAL PROCEEDINGS
 
  (a) Environmental Proceedings.
 
     RECENT DEVELOPMENTS RELATING TO PENDING CLAIMS SINCE THE END OF FISCAL YEAR
1997. As previously reported in the Company's annual report on Form 10-K for the
year ended December 31, 1997, the Company received a complaint on July 26, 1994
in GLIDDEN COMPANY ET AL. V. AMERICAN COLOR AND CHEMICAL ET AL., No. 94-C-3970,
filed in the United States District Court for the Eastern District of
Pennsylvania. The plaintiffs are five companies that, pursuant to orders issued
by the U.S. Environmental Protection Agency (the "U.S. EPA") under the
Comprehensive, Environmental, Response, Compensation and Liability Act
("CERCLA"), have been spending funds to secure, maintain and conduct an
investigation of the Berks Landfill in Sinking Springs, Pennsylvania (the "Berks
Site"). The plaintiffs are alleged to have disposed of wastes at the Berks Site,
which operated from 1950 through October 1, 1986. The 40 defendants (22 of which
were added in 1997) consist of former owners or operators of the Berks Site and
alleged transporters and/or generators of waste disposed of at the Berks Site.
It is believed that hundreds of other entities disposed of waste at the Berks
Site during its long period of operation. The plaintiffs seek to recover their
past and future costs pursuant to rights of contribution under CERCLA and the
Pennsylvania Hazardous Sites Cleanup Act. Plaintiffs allege that they have spent
approximately $3 million to secure and maintain the Berks Site and to prepare a
remedial investigation/feasibility study and a risk assessment. Discovery is
proceeding pursuant to a case management order. On September 30, 1997, the U.S.
EPA sent a special notice letter to the Company and 28 other entities, 7 of whom
are not parties to the Glidden litigation. The letter requested reimbursement of
the U.S. EPA's past costs (at least $755,959) and future costs relating to the
landfill, and solicited a proposal to conduct or finance the remedial action
selected by the U.S. EPA in its July 1997 Record of Decision, the present worth
cost of which is estimated by the U.S. EPA to be $6.1 million. The U.S. EPA
received no proposal in response to its letter. On March 31, 1998, the U.S. EPA
issued an administrative order to 18 entities, but not to the Company, directing
them to implement the remedy selected in the July 1997 Record of Decision. The
Company has been advised by the U.S. EPA that it is considered by the agency to
be a candidate for a de minimis settlement. The Company's expenses at the Berks
Site will be affected by a number of uncertainties, including the method and
extent of remediation, the percentage of waste disposed of at the Berks Site
attributable to the Company relative to that attributable to other parties, and
the financial capabilities of the other Potentially Responsible Persons (the
"PRPs").
 
     The Company was identified as one of the PRPs under CERCLA at the Spectron
Superfund Site in Elkton, Maryland (the "Elkton Site"). The Company reached a
settlement with the U.S. EPA resolving the Company's liability under the
Administrative Orders by Consent dated August 21, 1989 and October 1, 1991. The
cost of compliance with the terms of these Orders is approximately $8,480,000,
of which the Company's proportionate share is $20,461. On September 29, 1995,
the U.S. EPA sent a "Special Notice for Negotiations for Remedial
Investigation/Feasibility Study" to approximately 700 PRPs, including the
Company. The U.S. EPA estimates that the final remedy for the Elkton Site will
cost in the aggregate approximately $45 million. In October 1995, the terms of
several proposed de minimis settlement/buyout options designed to resolve all
remaining liability with respect to the Elkton Site were circulated among a
group of PRPs, including the Company. The Company indicated its willingness to
pursue resolution of its liability through a de minimis settlement/buyout. The
Company has received information from the PRP group negotiating with the U.S.
EPA that the terms of such a settlement will be circulated to qualifying PRPs
(including the Company) in the second or third quarter of 1998.
 
     The Company has advised the U.S. EPA and the Ohio Environmental Protection
Agency that it was unable to meet the December 1997 deadline for achieving
emission limitations for a solvent degreaser at its Elmore, Ohio plant. On April
17, 1998, the Company signed an administrative order issued on consent by the
U.S. EPA. This order imposes a timetable for achieving compliance with the
emission limitations and does not impose a penalty.
 
                                        9
<PAGE>   11
 
  (b) Beryllium Exposure Claims.
 
     RECENT DEVELOPMENTS RELATING TO PENDING CLAIMS SINCE THE END OF FISCAL YEAR
1997. As previously reported in the Company's annual report on Form 10-K for the
year ended December 31, 1997, nine Company employees and their spouses had filed
law suits against the Company and certain of its employees in the Superior Court
of Pima County, Arizona: COLE ET AL. V. BRUSH WELLMAN INC. ET AL.; CRUZ ET AL.
V. BRUSH WELLMAN INC. ET AL.; HAYNES-KERN ET AL. V. BRUSH WELLMAN INC. ET AL.;
MATULIN ET AL. V. BRUSH WELLMAN INC. ET AL.; FIMBRES ET AL. V. BRUSH WELLMAN
INC. ET AL.; FLORES ET AL. V. BRUSH WELLMAN INC. ET AL.; KOFIRA ET AL. V. BRUSH
WELLMAN INC. ET AL.; MALDONADO ET AL. V. BRUSH WELLMAN INC. ET AL.; AND STOECKER
ET AL. V. BRUSH WELLMAN INC. ET AL. Six of these suits were instituted on June
29, 1994; one was instituted on December 13, 1994; and two were instituted on
February 28, 1995. The plaintiffs claimed that, during their employment with the
Company, they contracted chronic beryllium disease ("CBD") as a result of
exposure to beryllium and beryllium-containing products. The plaintiffs sought
compensatory and punitive damages of an unspecified amount based on allegations
that the Company intentionally misrepresented the potential danger of exposure
to beryllium and breached an agreement to pay certain benefits should the
plaintiffs contract CBD. These nine cases were dismissed by the trial court
following summary judgments entered in favor of the Company on August 26, 1996.
The plaintiffs appealed the adverse ruling to the Arizona Court of Appeals. On
March 31, 1998, the Court of Appeals filed its decision, affirming in part and
reversing in part the summary judgments. The Court of Appeals held that all of
plaintiffs' common law claims -- breach of contract, breach of implied covenant
of good faith and fair dealing, and fraud -- were barred by the election of
remedy provision in Arizona statutory law. Thus, this portion of the summary
judgments was affirmed. The Court of Appeals further held that, under Arizona
law, a constitutionally protected claim for willful misconduct existed which was
not waived by plaintiffs' acceptance of workers compensation benefits and that a
question of fact existed as to whether that claim was barred by the statute of
limitations. The Court made no ruling on whether there was any merit to any such
claim by the plaintiffs. Defense of all of these cases is being conducted by
counsel retained by the Company, and the Company believes that resolution of
these cases will not have a material adverse effect on the Company.
 
     As previously reported in the Company's annual report on Form 10-K for the
year ended December 31, 1997, the Company is a defendant in seven cases pending
before the Court of Common Pleas of Cuyahoga County, Ohio, brought by current
and former employees of the Company and, in most of the cases, their family
members: BERLIN V. BRUSH WELLMAN INC., filed January 24, 1997; KNEPPER ET AL. V.
BRUSH WELLMAN INC., filed January 23, 1997; MIA JOHNSON, EXECUTRIX OF THE ESTATE
OF ETHEL JONES ET AL. V. BRUSH WELLMAN INC., filed January 22, 1997; JACOBS ET
AL. V. BRUSH WELLMAN INC., filed December 31, 1996; STARIN V. BRUSH WELLMAN
INC., filed December 31, 1996; MUSSER ET AL. V. BRUSH WELLMAN INC., filed
October 25, 1996; and WHITAKER ET AL. V. BRUSH WELLMAN INC., filed August 23,
1996. The complaints in all of these cases allege that the employees contracted
CBD at the workplace, seek recovery on an intentional tort theory and, except in
the Berlin and Starin cases, include claims by family members. The plaintiffs in
these cases seek both compensatory and, except in the Knepper case, punitive
damages. All of these cases, except the Knepper case, have been consolidated at
least for purposes of discovery and pretrial motions, and all are set for trial
in June 1998. The consolidation order of the Court indicates that, after
discovery, the Court will revisit whether the cases should be consolidated for
trial. On October 6, 1997, the Company filed a motion to dismiss or in the
alternative for summary judgment in the Knepper case. This motion remains
pending. On October 16, 1997, one of the employee-plaintiffs in the consolidated
cases and his spouse dismissed their complaint without prejudice. On November
26, 1997, the Company filed a motion for summary judgment in the Starin case.
This motion remains pending. On March 20, 1998, the parties filed an agreed
motion to stay and to cancel all scheduled events in all of the seven cases on
the grounds that the parties had negotiated a settlement and would need time to
reduce that settlement to definitive written agreements. In addition, certain
aspects of the proposed settlement are to be submitted for approval of the
probate divisions of the appropriate common pleas courts. The motion to stay was
granted on March 30, 1998, but the Court left in place the June 22, 1998 trial
date. No assurance can be given that the settlement will be effected as
currently anticipated since the
                                       10
<PAGE>   12
 
agreements have not yet all been signed, or, where necessary, submitted to the
appropriate probate court. The Company believes that resolution of these cases
will not have a material adverse effect on the Company.
 
  (c) Asbestos Exposure Claims.
 
     A subsidiary of the Company (the "Subsidiary") is a co-defendant in
eighteen cases making claims for asbestos-induced illness allegedly relating to
the former operations of the Subsidiary, then known as The S.K. Wellman Corp.
All of these cases have been reported in prior filings with the S.E.C. In all
but a small portion of these cases, the Subsidiary is one of a large number of
defendants in each case. The plaintiffs seek compensatory and punitive damages,
in most cases of unspecified sums. Each case has been referred for defense
pursuant to liability insurance coverage and has been accepted for defense
without admission or denial of carrier liability. Two hundred forty-eight
similar cases previously reported have been dismissed or disposed of by pretrial
judgment, one by jury verdict of no liability and fourteen others by settlement
for nominal sums. The Company believes that resolution of the pending cases
referred to in this paragraph will not have a material adverse effect on the
Company.
 
     The Subsidiary is a party to an agreement with the predecessor owner of its
operating assets, Pneumo Abex Corporation (formerly Abex Corporation), and five
insurers, regarding the handling of these cases. Under the agreement, the
insurers share expenses of defense, and the Subsidiary, Pneumo Abex Corporation
and the insurers share payment of settlements and/or judgments. In certain of
the pending cases, both expenses of defense and payment of settlements and/or
judgments are subject to a limited, separate reimbursement agreement with MLX
Corp., the parent of the company that purchased the Subsidiary's operating
assets in 1986.
 
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<PAGE>   13
 
ITEM 6. EXHIBITS AND REPORTS ON FORM 8-K
 
  (a) Exhibits
 
     11. Statement re: computation of per share earnings.
 
     27. Financial Data Schedule.
 
  (b) Reports on Form 8-K
 
     There have been no reports on Form 8-K during the quarter ended April 3,
1998.
 
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<PAGE>   14
 
                                   SIGNATURES
 
     PURSUANT TO THE REQUIREMENTS OF THE SECURITIES EXCHANGE ACT OF 1934, THE
REGISTRANT HAS DULY CAUSED THIS REPORT TO BE SIGNED ON ITS BEHALF BY THE
UNDERSIGNED THEREUNTO DULY AUTHORIZED.
 
                                          BRUSH WELLMAN INC.
Dated: May 15, 1998
                                          /s/ Carl Cramer
 
                                          --------------------------------------
                                          Carl Cramer
                                          Vice President Finance and
                                          Chief Financial Officer
 
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