<PAGE>   1
                       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 4, 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 1-8769
                                                 ------

                             R. G. BARRY CORPORATION
                             -----------------------
             (Exact name of registrant as specified in its charter)

                OHIO                                  31-4362899
                ------------------------------------------------
        (State or other jurisdiction               (IRS Employer
      of incorporation or organization)          Identification Number)

     13405 Yarmouth Road NW, Pickerington, Ohio                43147
     ---------------------------------------------------------------
      (Address of principal executive office)               (Zip Code)

                                  614-864-6400
                                  ------------
              (Registrant's telephone number, including area code)

                                 NOT APPLICABLE
                                 --------------
 (Former name, former address, and former fiscal year, if changed since last 
report)

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      
                              ---------     ----------

    Common Shares, $1 Par Value, Outstanding as of April 4, 1998 - 9,596,376



                          Index to Exhibits at page 10

                               Page 1 of 12 pages


<PAGE>   2

                         PART I - FINANCIAL INFORMATION
                          ITEM 1 - FINANCIAL STATEMENTS
                    R. G. BARRY CORPORATION AND SUBSIDIARIES
                           CONSOLIDATED BALANCE SHEETS
<TABLE>
<CAPTION>

                                                               April 4, 1998         January 3, 1998
                                                                ------------         ---------------
ASSETS:                                                                     (in thousands)
<S>                                                                 <C>                       <C>   
   Cash and cash equivalents                                        $  6,255                  22,495
   Accounts receivable, less allowances                               13,498                  16,961
   Inventory (note 3)                                                 46,336                  35,602
   Deferred income taxes (note 4)                                      4,827                   4,827
   Recoverable income taxes                                              447
   Prepaid expenses                                                    2,160                   2,669
                                                                      ------                  ------
         Total current assets                                         73,523                  82,554
                                                                      ------                  ------

   Property, plant and equipment, at cost                             41,668                  40,840
      Less accumulated depreciation & amortization                    27,224                  26,609
                                                                      ------                  ------
         Net property, plant and equipment                            14,444                  14,231
                                                                      ------                  ------

   Goodwill, net of amortization                                       4,201                   4,230
   Other assets                                                        3,725                   3,659
                                                                      ------                  ------
                                                                     $95,893                 104,674
                                                                     =======                 =======

LIABILITIES AND SHAREHOLDER'S EQUITY:
   Current installments of long-term debt
      and capital lease obligations                                    2,273                   2,273
   Accounts payable                                                    6,766                   6,389
   Accrued expenses                                                    2,579                  11,355
                                                                       -----                  ------
      Total current liabilities                                       11,618                  20,017
                                                                      ------                  ------

   Accrued retirement costs and other, net                             4,284                   4,057
   Long-term debt and capital lease obligations,
      excluding current installments:
      Note payable                                                    12,857                  12,857
      Capital lease obligations                                          135                     135
                                                                     -------                 -------
         Long-term debt and capital lease obligations                 12,992                  12,992
                                                                      ------                  ------
            Total liabilities                                         28,894                  37,066
                                                                      ------                  ------

   Shareholders' equity:
      Preferred shares, $1 par value
         Authorized 3,775,000 Class A shares, 
           225,000 Series I Junior
           Participating Class A Shares, 
           and 1,000,000 Class B shares, none issued
      Common shares, $1 par value
         Authorized 22,500,000 shares
         (excluding treasury shares)                                   9,596                   9,564
      Additional capital in excess of par value                       14,969                  14,629
      Deferred compensation (note 6)                                (    230)                      -
      Retained earnings                                               42,664                  43,415
                                                                      ------                  ------
         Net shareholders' equity                                     66,999                  67,608
                                                                      ------                  ------
                                                                    $ 95,893                 104,674
                                                                    ========                 =======
</TABLE>



                               Page 2 of 12 pages
<PAGE>   3

                    R. G. BARRY CORPORATION AND SUBSIDIARIES
                      CONSOLIDATED STATEMENTS OF OPERATIONS

<TABLE>
<CAPTION>

                                                                               Thirteen           Thirteen
                                                                              weeks ended        weeks ended
                                                                                April 4,           March 29,
                                                                                -------            ---------
                                                                                 1998                1997
                                                                                 ----                ----
                                                                                       (in thousands)
<S>                                                                            <C>                 <C>   
Net sales                                                                      $15,593             14,963
Cost of sales                                                                    5,446              6,604
                                                                                 -----              -----
   Gross profit                                                                 10,147              8,359
Selling, general and
   administrative expense                                                       11,337             10,087
                                                                                ------             ------
Operating loss                                                                  (1,190)            (1,728)

Other income                                                                       104                145

Interest expense                                                                  (383)              (377)
Interest income                                                                    217                171
                                                                                  ----               ----
   Net interest expense                                                           (166)              (206)

Loss before
   tax benefit                                                                  (1,252)            (1,789)
Income tax benefit (note 4)                                                       (501)            (  716)
                                                                              ---------          ---------
   Net loss                                                                     ($ 751)            (1,073)
                                                                               ========           ========

Net loss per common share (note 5)
      Basic                                                                    ($ 0.08)           ($ 0.11)
                                                                               ========           ========
      Diluted                                                                  ($ 0.08)           ($ 0.11)
                                                                               ========           ========

Average number of common
   shares outstanding
      Basic                                                                      9,599              9,413
                                                                                 =====              =====
      Diluted                                                                    9,599              9,413
                                                                                 =====              =====
</TABLE>

                               Page 3 of 12 pages
<PAGE>   4

                    R. G. BARRY CORPORATION AND SUBSIDIARIES
                 CONDENSED CONSOLIDATED STATEMENTS OF CASH FLOW
<TABLE>
<CAPTION>

                                                                               Thirteen           Thirteen
                                                                             weeks ended         weeks ended
                                                                               April 4,           March 29,
                                                                               --------           ---------
                                                                                 1998               1997
                                                                                 ----               ----
                                                                                      (in thousands)
<S>                                                                           <C>                 <C>     
Cash flows from operating activities:
   Net loss                                                                   ($  751)             (1,073)
   Adjustments to reconcile net loss to net cash
      used in operating activities:
      Depreciation and amortization of
         property, plant and equipment                                            495                 424
      Amortization of goodwill                                                     29                  29
      Net (increase) decrease in:
         Accounts receivable, net                                               3,463               7,103
         Inventory                                                            (10,734)             (8,575)
         Prepaid expenses                                                         509                 (98)
         Recoverable income taxes                                                (447)               (678)
         Other                                                                    (66)                 31
      Net increase (decrease) in:
         Accounts payable                                                         377               1,732
         Accrued expenses                                                      (8,776)             (7,498)
         Accrued retirement costs and other                                       227                 220
                                                                            ---------           ---------
            Net cash used in operating activities                             (15,674)             (8,383)
                                                                              --------            --------


Cash flows from investing activities:
   Additions to property, plant and equipment, net                               (708)               (592)
                                                                              --------            --------


Cash flows from financing activities:
   Stock options exercised, net of treasury acquisitions                          372                 238
   Common shares granted as deferred compensation                                (230)                  0
                                                                               -------           --------
         Net cash provided by financing activities                                142                 238
                                                                               ------              ------

Net decrease in cash                                                          (16,240)             (8,737)
Cash at the beginning of the period                                            22,495              13,187
                                                                               ------              ------
Cash at the end of the period                                                 $ 6,255             $ 4,450
                                                                              =======             =======

Supplemental cash flow disclosures:
   Interest paid                                                             $    769                 742
                                                                             ========              ======
   Income taxes paid                                                          $ 6,344               3,442
                                                                              =======               =====

</TABLE>

                               Page 4 of 12 pages

<PAGE>   5

                    R. G. BARRY CORPORATION AND SUBSIDIARIES
                          Notes to Financial Statements
                       Under Item 1 of Part I of Form 10-Q
             for the periods ended April 4, 1998 and March 29, 1997

1.   The interim financial statement are unaudited. All adjustments (consisting
     solely of normal recurring adjustments) have been made which, in the
     opinion of management, are necessary to fairly present the results of
     operations.

2.   The Company operates on a fifty-two or fifty-three week annual fiscal year.
     Fiscal 1998 is a fifty-two week year, whereas, fiscal 1997 was a
     fifty-three week year.

3.   A substantial portion of inventory is valued using the dollar value LIFO
     method and, therefore, it is impractical to separate inventory values
     between raw materials, work-in-process and finished goods.

4.   Income tax benefit for the periods ended April 4, 1998 and March 29, 1997 
     consisted of:
<TABLE>
<CAPTION>
                                                                1998                 1997
                                                                ----                 ----
<S>                                                              <C>                 <C>       
                     Current:
                          U. S. Federal benefit                  ($   427)           ($    605)
                          State & Local                          (     74)           (     111)
                                                                 ---------           ----------
                               Total                             ($   501)           ($    716)
                                                                 =========           ==========
</TABLE>


     The income tax benefit reflects a combined federal, foreign, state and 
     local effective rate of 40.0 percent for the first quarter of both years, 
     as compared to the statutory U. S. federal rate of 35.0 percent in both 
     years.

     Income tax for the periods ended April 4, 1998 and March 29, 1997 differed
     from the amounts computed by applying the U. S. federal income tax rate of 
     35.0 percent to pretax loss as a result of the following:
<TABLE>
<CAPTION>
                                                                1998                  1997
                                                                ----                  ----
<S>                                                               <C>                  <C>     
                     Computed "expected"
                       tax benefit:
                          U. S. Federal benefit                   ($  439)             ($  608)
                          Other                                   (    14)             (    35)
                          State & Local benefit, net of
                            federal income tax benefit            (    48)             (    73)
                                                                  --------             --------
                               Total                              ($  501)             ($  716)
                                                                  ========             ========
</TABLE>

5.   The computation of basic loss per common share has been computed based on 
     the weighted average number of common shares outstanding during each 
     period. Diluted loss per common share is based on the weighted average 
     number of outstanding common shares during the period, plus, when their 
     effect is dilutive, potential common shares consisting of certain common 
     shares subject to stock options and the stock purchase plan.

6.   Pursuant to agreements with two key executives, entered into in January
     1998, the Company is committed to issue a total of 10,000 common shares to
     each executive ratably over the next eight years, subject to the terms of
     the agreement. Upon achievement of certain profit goals in any fiscal year,
     the issuance of common shares may be accelerated. The Company will expense
     the costs associated with the agreements over the eight year term of the
     agreements.

                               Page 5 of 12 pages
<PAGE>   6

                    R. G. BARRY CORPORATION AND SUBSIDIARIES
      ITEM 2 - Management's Discussion and Analysis of Financial Condition
                            and Results of Operations

Liquidity and Capital Resources
-------------------------------
The Company ended the first quarter of 1998 with $61.9 million in net working
capital. This compares with $53.0 million at the end of the same quarter in
1997, and $62.5 million as of the end of the 1997 fiscal year. The increase in
net working capital from the end of the first quarter of 1997 to the end of the
first quarter of 1998, is primarily due to the profit that the Company earned
during fiscal 1997. The decline in working capital from fiscal year end 1997 to
the end of the first quarter of 1998, is mainly the result of the seasonal loss
in the first quarter of 1998.

A review of the principal components of the Company's net working capital
indicates:
*    Accounts receivable increased from $11.5 million at the end of the first
     quarter of 1997, to $13.5 million at the end of the first quarter of 1998,
     and decreased from $17.0 million at the end of fiscal 1997. The increase in
     receivables from first quarter 1997 to 1998, is mainly due to an increase
     in sales during the first quarter of 1998 when compared with the same
     quarter of 1997. The decrease in receivables from the end of fiscal 1997 to
     the end of the first quarter of 1998, mainly represents a normal seasonal
     pattern of change in receivables. 
*    Inventories ended the first quarter of 1998, at $46.3 million compared with
     $37.4 million one year ago, and $35.6 million as of the end of fiscal 1997.
     As of year end 1997, the Company had inventories that were $6.7 million
     more than as of year end 1996. Most of that increase in inventory, (as well
     as the increase in inventory at the end of the first quarter 1998 when
     compared with the first quarter of 1997) was spread among the various
     elements of inventory - materials, in-process, and finished goods, and
     spread among slippers as well as thermal products. The Company is
     comfortable with this level of inventory as it builds its operations in
     Europe and plans for future growth in its domestic business. The increase
     in inventories from the end of fiscal 1997 to the end of the first quarter
     1998, reflects a normal seasonal pattern of inventory growth, as the
     Company prepares for its anticipated needs later in the year.
*    The Company ended the first quarter of 1998, with $6.3 million in cash and
     equivalents. This compares with the first quarter of 1997, when the Company
     had $4.5 million in cash and equivalents. There were no short-term seasonal
     bank loans outstanding during either quarter. The Company ended fiscal 1997
     with $22.5 million in cash and cash equivalents.

The Company's capital expenditures during the first quarter of 1998, amounted to
$708 thousand, compared with $592 thousand during the same period of 1997.
Capital expenditures in both years were funded out of working capital.

The Company currently has in place a Revolving Credit Agreement ("Revolver"),
with its three main lending banks. The Revolver provides the Company a
seasonally adjusted available line of credit ranging from $6 million during
January, to a peak of $51 million from July through November. The Revolver
contains financial covenants typical of agreements of its type and duration. The
Company is in compliance with all the covenants of the Revolver, and all other
debt agreements. The Revolver currently extends through 1999 and provides for
periodic extensions upon request and with the approval of the banks. The Company
intends to request an extension through 2000, and anticipates the banks granting
an extension.

Year 2000 Considerations
------------------------
As noted in the Company's 1997 Annual Report to Shareholders, the Company has
conducted a review of its key financial, information and operating systems. The
Company believes that all of its critical applications systems have been
converted to correct for potential problems. Additional tests conducted in 1998,
have confirmed the efficacy of the conversion.


                               Page 6 of 12 pages
<PAGE>   7

           Management's Discussion and Analysis of Financial Condition
                      and Results of Operations - continued

Results of Operations
---------------------
During the first quarter of 1998, net sales amounted to $15.6 million, a 4.2
percent increase in net sales from the $15.0 million during the first quarter of
1997. Gross shipments to customers, i.e. sales to customers before consideration
of customer returns processed during the quarter, increased by 12.4 percent,
from $20.3 million in the first quarter of 1997 to $22.8 million during the
first quarter of 1998. Returns from customers reduced the increase in net sales
to 4.2 percent. The Company accrued for the estimated profit impact of returns
during the fourth quarter of 1997.

Gross profit during the first quarter of 1998, amounted to $10.1 million on
$15.6 million in net sales, or 65.1 percent of net sales. This compares with
gross profit of $8.4 million on $15.0 million in net sales in the same quarter
of 1997, or 55.9 percent of net sales. The increase in gross profit percentages
from year to year, is due to a change in mix of individual styles and products
sold from one period to the other, and from continued cost reductions realized
as a result of improved materials utilization and improved efficiencies realized
from the use of modular manufacturing, and the increase in returns processed in
the first quarter of 1998.

Selling, general and administrative expenses during the quarter, at $11.3
million, represent an increase of 12.4 percent from similar expenses incurred
during the first quarter of 1997. The increase in these expenses is consistent
with the increase in sales. Nearly one-half of the increase in selling, general
and administrative expense relates to the sales and marketing expenses incurred
in Europe in support of the Company's expanded operations there.

Net interest expense declined from 1997 to 1998. During the first quarter of
1998, net interest expense amounted to $166 thousand compared with $206 thousand
in the first quarter of 1997. As a result of improved liquidity during the first
quarter of 1998, the Company had more excess funds from which to earn more
interest income on short-term instruments in 1998 than during the first quarter
of 1997.

For the first quarter of 1998, the Company incurred a loss of $751 thousand, or
$0.08 per share, compared with a loss during the same quarter of 1997 of $1.1
million, or $0.11 per share. Per share calculations from both years are the same
for both basic loss per share and for diluted loss per share.

--------------------------------------------------------------------------------
"SAFE HARBOR" STATEMENT UNDER THE PRIVATE SECURITIES LITIGATION REFORM ACT OF
1995:
The statements in this Quarterly Report on Form 10-Q, which are not historical
fact are forward looking statements based upon the Company's current plans and
strategies, and reflect the Company's current assessment of the risks and
uncertainties related to its business, including such things as product demand
and market acceptance; the economic and business environment and the impact of
governmental regulations, both in the United States and abroad; the effects of
competitive products and pricing pressures; currency risks; capacity,
efficiency, and supply constraints; weather conditions; and other risks detailed
in the Company's press releases, shareholder communications, and Securities and
Exchange Commission filings. Actual events affecting the Company and the impact
of such events on the Company's operations may vary from those currently
anticipated.
--------------------------------------------------------------------------------


             ITEM 3 - Quantitative and Qualitative Disclosures About Market Risk
Not Applicable

                               Page 7 of 12 pages

<PAGE>   8

                           PART II - OTHER INFORMATION


Item 1.  Legal proceedings
--------------------------
                  No response required

Item 2.  Changes in Securities and Use of Proceeds
--------------------------------------------------
                  (a) through (c) Not Applicable

Item 3.  Defaults Upon Senior Securities
----------------------------------------
                  (a), (b) Not Applicable

Item 4.  Submission of Matters to a Vote of Security Holders
------------------------------------------------------------
                  (a) - (d) Not Applicable

Item 5.  Other Information
--------------------------
                  No response required

Item 6. Exhibits and Reports on Form 8-K
----------------------------------------
                  (a) Exhibits: See Index to Exhibits at page 10.
                  ------------

                  (b) REPORTS ON FORM 8-K: On March 13, 1998, the Company filed
                  a report on Form 8-K regarding the Company's approval of an 
                  extension of the benefits afforded by the Company's existing 
                  Shareholder Rights Plan by adopting a new Shareholder Rights 
                  Plan ("Plan"). The Plan will expire, on March 16, 2008, unless
                  the Rights are earlier redeemed or the Plan is extended.



                               Page 8 of 12 pages
<PAGE>   9


                                   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.







                                                R. G. BARRY CORPORATION
                                                -----------------------
                                                Registrant

May 15, 1998
------------
    date
                                                 /s/ Richard L. Burrell
                                                 -------------------------------
                                                 Richard L. Burrell
                                                 Senior Vice President - Finance
                                                 (Principal Financial Officer)
                                                 (Duly Authorized Officer)


                               Page 9 of 12 pages
<PAGE>   10

                             R. G. BARRY CORPORATION

                                INDEX TO EXHIBITS
<TABLE>
<CAPTION>

      Exhibit Number                     Description                              Page Number
      --------------                     -----------                              -----------

<S>                         <C>                                     <C>
            4               Rights Agreement, dated as of           Incorporated by reference to Exhibit 4
                            February 19, 1998, between R. G.        of the Registrant's Current Report of
                            Barry Corporation and The Bank of New   Form 8-K, as filed on March 13, 1998
                            York, which includes as Exhibit B       (File Number 1-8769)
                            thereto, the Form of Rights
                            Certificate

           27.1             Financial Data Schedule                                   11
                            (Period ended April 4, 1998)

           27.2             Financial Data Schedule                                   12
                            (Period ended March 29, 1997 Restated)

</TABLE>

                               Page 10 of 12 pages