<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         October 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 1-8769
                                                 ------

                             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 offices)                (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 October 3, 1998 - 9,741,965
                                                  ---------------------------


                          Index to Exhibits at page 11

                               Page 1 of 13 pages
<PAGE>   2
<TABLE>
                               PART I - FINANCIAL INFORMATION
                                ITEM 1 - FINANCIAL STATEMENTS
                          R. G. BARRY CORPORATION AND SUBSIDIARIES
                                 CONSOLIDATED BALANCE SHEETS
<CAPTION>
                                                           October 3, 1998  January 3, 1998
                                                           ---------------  ---------------
                                                                     (in thousands)
<S>                                                        <C>              <C>   
ASSETS:
   Cash and cash equivalents                                   $  2,678          22,495
   Accounts receivable, less allowances                          43,354          16,961
   Inventory (note 3)                                            51,714          35,602
   Deferred income taxes                                          4,827           4,827
   Prepaid expenses                                               2,671           2,669
                                                               --------         -------
         Total current assets                                   105,244          82,554
                                                               --------         -------

   Property, plant and equipment, at cost                        41,556          40,840
      Less accumulated depreciation & amortization               28,239          26,609
                                                               --------         -------
         Net property, plant and equipment                       13,317          14,231
                                                               --------         -------

   Goodwill, less accumulated amortization                        4,144           4,230
   Other assets                                                   3,205           3,659
                                                               --------         -------
                                                               $125,910         104,674
                                                               ========         =======

LIABILITIES AND SHAREHOLDERS' EQUITY:
   Current installments of long-term debt
      and capital lease obligations                               2,273           2,273
   Short-term notes payable                                      24,000              --
   Accounts payable                                               7,153           6,389
   Accrued expenses                                               5,181          11,355
                                                               --------         -------
      Total current liabilities                                  38,607          20,017
                                                               --------         -------

   Accrued retirement costs and other, net                        4,655           4,057

   Long-term debt and capital lease obligations,
      excluding current installments:
      Note payable                                               10,714          12,857
      Capital lease obligations                                     135             135
                                                               --------         -------
         Long-term debt and capital lease obligations            10,849          12,992
                                                               --------         -------
            Total liabilities                                    54,111          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)                              9,742           9,564
      Additional capital in excess of par value                  15,137          14,629
      Deferred compensation (note 6)                               (211)             --
      Retained earnings                                          47,131          43,415
                                                               --------         -------
         Net shareholders' equity                                71,799          67,608
                                                               --------         -------
                                                               $125,910         104,674
                                                               ========         =======
</TABLE>

                               Page 2 of 13 pages
<PAGE>   3
<TABLE>
                       R. G. BARRY CORPORATION AND SUBSIDIARIES
                         CONSOLIDATED STATEMENTS OF OPERATIONS
<CAPTION>
                                       Thirteen weeks ended  Thirty-nine weeks ended
                                       --------------------  -----------------------
                                       Oct. 3,   Sept. 27,     Oct. 3,   Sept. 27,
                                          1998        1997        1998        1997
                                          ----        ----        ----        ----
                                                      (in thousands)
<S>                                    <C>       <C>           <C>       <C>
Net sales                              $57,184      46,361      89,687      75,835
Cost of sales                           30,215      24,611      43,841      38,838
                                       -------      ------      ------      ------
   Gross profit                         26,969      21,750      45,846      36,997

Selling, general and
   administrative expense               16,460      12,815      38,900      32,479
                                       -------      ------      ------      ------
Operating income                        10,509       8,935       6,946       4,518

Other income                               102         111         293         354

Interest expense                          (675)       (693)     (1,459)     (1,520)
Interest income                             11          19         252         222
                                       -------      ------      ------      ------
   Net interest expense                   (664)       (674)     (1,207)     (1,298)

Earnings before
   income taxes                          9,947       8,372       6,032       3,574
Income tax expense (note 4)              3,882       3,348       2,316       1,429
                                       -------      ------      ------      ------
   Net earnings                        $ 6,065       5,024       3,716       2,145
                                       =======      ======      ======      ======

Earnings per common share (note 5)
      Basic                            $  0.62        0.52        0.38        0.22
                                       =======      ======      ======      ======
      Diluted                          $  0.61        0.52        0.37        0.22
                                       =======      ======      ======      ======

Average number of common
   shares outstanding
      Basic                              9,733       9,552       9,676       9,484
                                       =======      ======      ======      ======
      Diluted                           10,050       9,906      10,004       9,800
                                       =======      ======      ======      ======
</TABLE>

                               Page 3 of 13 pages
<PAGE>   4
<TABLE>
                           R. G. BARRY CORPORATION AND SUBSIDIARIES
                        CONDENSED CONSOLIDATED STATEMENTS OF CASH FLOW
<CAPTION>
                                                               Thirty-nine       Thirty-nine
                                                               weeks ended       weeks ended
                                                              Oct. 3, 1998    Sept. 27, 1997
                                                              ------------    --------------
                                                                     (in thousands)
<S>                                                           <C>             <C>  
Cash flows from operating activities:
   Net earnings                                                 $  3,716           2,145
   Adjustments to reconcile net earnings to net cash
      used in operating activities:
      Depreciation and amortization of
         property, plant and equipment                             1,510           1,322
      Amortization of goodwill                                        86              86
      Net (increase) decrease in:
         Accounts receivable, net                                (26,393)        (14,142)
         Inventory                                               (16,112)        (20,041)
         Prepaid expenses                                             (2)         (1,401)
         Other                                                       454             (70)
      Net increase (decrease) in:
         Accounts payable                                            764           2,840
         Accrued expenses                                         (6,174)         (5,658)
         Accrued retirement costs and other                          598             603
                                                                --------         -------
            Net cash used in operating activities                (41,553)        (34,316)
                                                                --------         -------

Cash flows from investing activities:
   Additions to property, plant and equipment, net                  (596)         (1,675)
                                                                --------         -------

Cash flows from financing activities:
   Proceeds from short-term notes                                 24,000          24,000
   Stock options exercised, net of treasury acquisitions             475             594
   Repayment of long-term debt and
      capital lease obligations                                   (2,143)              0
                                                                --------         -------
         Net cash provided by financing activities                22,332          24,594
                                                                --------         -------

Net decrease in cash                                             (19,817)        (11,397)
Cash at the beginning of the period                               22,495          13,187
                                                                --------         -------
Cash at the end of the period                                   $  2,678           1,790
                                                                ========         =======

Supplemental cash flow disclosures:
   Interest paid                                                $  1,733           1,705
                                                                ========         =======
   Income taxes paid                                            $  6,751           3,770
                                                                ========         =======
</TABLE>

                               Page 4 of 13 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
                     October 3, 1998 and September 27, 1997

1.   These interim financial statements 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, 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 for the periods ended October 3, 1998 and September 27, 1997,
     consists of:

                                                  1998          1997
                                                  ----          ----
                     Current:
                          U. S. Federal          $2,166        $1,204
                          State & Local             150           225
                                                 ------        ------
                               Total             $2,316        $1,429
                                                 ======        ======

     The income tax reflects a combined federal, foreign, state and local
     effective rate of 38.4 percent in 1998 and 40.0 percent in 1997, as
     compared to the statutory U. S. federal rate of 35.0 percent in both years.

     Income tax for the periods ended October 3, 1998 and September 27, 1997
     differed from the amounts computed by applying the U. S. federal income tax
     rate of 35.0 percent to pretax earnings as a result of the following:

                                                         1998         1997
                                                         ----         ----
                     Computed "expected" tax:
                          U. S. Federal                 $2,111       $1,215
                          Other                            107           63
                          State & Local, net of
                            federal income tax              98          151
                                                        ------       ------
                               Total                    $2,316       $1,429
                                                        ======       ======


5.   The computation of basic earnings per common share has been computed based
     on the weighted average number of common shares outstanding during each
     period. Diluted earnings 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 13 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 third quarter of 1998 with $66.6 million in net working
capital. This compares with $54.6 million at the end of the same quarter in
1997, and $62.5 million at the end of fiscal 1997. The increase in net working
capital from the end of the third quarter of 1997 to the end of the third
quarter of 1998, is mostly due to the profit that the Company earned during the
latest 12 months. The increase in working capital from fiscal year end 1997 to
the end of the third quarter of 1998, is mainly the result of the seasonal
profit earned during the first nine months of 1998, net of the scheduled
periodic payment on long-term debt made during the period.

Highlights of the significant changes in the components of the Company's net
working capital are:
o    Accounts receivable increased at the end of the third quarter of 1998, to
     $43.4 million from $32.7 million at the end of the third quarter of 1997,
     and increased from $17.0 million at the end of fiscal 1997. The increase in
     receivables from third quarter 1997 to the third quarter of 1998, is mainly
     due to the $10.8 million increase in net sales, or 23.3 percent, during the
     third quarter of 1998 when compared with the same quarter of 1997. The
     increase from the end of fiscal 1997, represents a normal seasonal pattern
     of change in receivables.
o    Inventories at the end of the third quarter of 1998, at $51.7 million, are
     about 5.8 percent greater than the inventory levels of $48.9 million one
     year ago, and increased from $35.6 million as of the end of fiscal 1997.
     The increase in inventories from the end of the third quarter of 1997 to
     the end of the third quarter of 1998 is primarily an increase in finished
     goods inventories, to support the increase in net sales from 1997 to 1998,
     as the Company builds its operations in Europe and plans for its
     anticipated future domestic growth. The increase in inventories from the
     end of fiscal 1997, reflects a normal seasonal increase.
o    The Company ended the third quarter of 1998, with $2.7 million in cash and
     $24 million in short-term bank loans. This compares with the third quarter
     of 1997, when the Company had $1.8 million in cash and the same $24 million
     in short-term bank loans. The increase in cash is largely the result of
     increased profitability in 1998 versus 1997, offset by the $2.1 million
     scheduled periodic payment on long-term debt made during 1998. There were
     no short-term bank loans outstanding at the end of fiscal 1997.

The Company's net capital expenditures during the first nine months of 1998,
amounted to $596 thousand, compared with $1.7 million during the same period of
1997. Capital expenditures in both years have been funded out of working
capital.

During the first quarter of 1999, the Company plans to open a new slipper
manufacturing facility in the Dominican Republic. This facility when fully
operational will produce all the components necessary to make a slipper and
assemble them into a finished product. Products produced in this plant will
enjoy duty-free entry into both Europe and the United States. The Company also
plans to open a 150,000 square foot distribution center in San Antonio, Texas in
early 1999. This new distribution center will allow the Company to move out of
several temporary storage locations and help better serve retail slipper
customers. Costs of opening both the manufacturing facility in the Dominican
Republic and the distribution center in San Antonio will be funded internally
from 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 extends through 2000 and contains provisions for
periodic extensions upon request and with the approval of the banks.

                               Page 6 of 13 pages
<PAGE>   7
           Management's Discussion and Analysis of Financial Condition
                      and Results of Operations - continued

Introduction of the "Euro" as a Common Legal Currency in Europe
---------------------------------------------------------------
The Company believes that it is prepared for the introduction of the "Euro" as
the common legal currency in certain European Community countries in 1999. The
United Kingdom, which is the Company's principle base of operations in Europe,
will not immediately join the transition to the Euro; although France, where the
Company also conducts business, will join. The Company's systems have been
designed with sufficient flexibility to handle the introduction of the Euro as a
transactional currency. The Company incurred a nominal cost in preparing itself
for the Euro.

Year 2000 Considerations
------------------------
The Company has conducted a review of its key financial, information and
operating systems to determine the extent to which it is exposed to year 2000
computer date problems. The Company believes that all of its critical
application systems have been converted to correct for potential date problems.
During the first quarter of 1998, the Company conducted extensive testing which
have confirmed its readiness. Key suppliers and electronic trading partners have
been contacted to obtain their commitments to conversion and readiness, so as to
minimize problems relating to the exchange of electronic data. The Company has
not separately identified the costs associated with this conversion, but
estimates that the costs incurred to date, which have been expensed as incurred,
have not been significant, and does not anticipate the future impact on its
financial condition, results of operations or cash flows will be material. The
possibility exists that the Company's conversion could inadvertently fail,
although the Company believes that the impact of such an occurrence would be
manageable and minor in impact as a result of substantial equipment and software
upgrades implemented in recent years. The Company is not dependent upon any one
customer or any one supplier to conduct its business, and the Company believes
that should one of its suppliers or customers prove not to become year 2000
compliant in a timely manner, the Company can convert to alternative compliant
suppliers or resort to increased use of paper transactions to satisfied its
customer needs. If in the future, the Company uncovers additional risks
associated with year 2000 compliance, the Company will develop contingency plans
at that time as deemed necessary.

Results of Operations
---------------------
During the third quarter of 1998, net sales amounted to $57.2 million, an
increase of 23.3 percent from net sales of $46.4 million during the third
quarter of 1997. For the nine months, net sales amounted to $89.7 million, an
18.3 percent increase in net sales when compared with the first nine months of
1997. Net sales of the Company's slipper products, domestically and
internationally, were responsible for substantially all of the increase in
consolidated net sales.

In 1997, we reported that raw material delivery and production scheduling
problems caused approximately $4 million of third quarter slipper orders to be
carried forward into the fourth quarter of 1997. Since third quarter 1998 sales
and earnings reflect complete and on-time deliveries of orders, the fourth
quarter of 1998 is not expected to reflect, as did the fourth quarter of 1997,
the impact from delayed deliveries. In addition, the Company has decided to
de-emphasize the sale of thermal consumer products in the accessories
departments of department stores, and as a result the Company expects fourth
quarter 1998 sales to be less that those reported for 1997.

Gross profit during the third quarter of 1998, amounted to $27.0 million, or
47.2 percent of net sales. This compares with gross profit percent of 46.9
percent in the same quarter of 1997. For the nine months, gross profit percent
also increased to 51.1 percent in 1998 compared with 48.8 percent in 1997. The
increase in gross profit percentages from year to year continues to result
mainly from the Company's continuing efforts in the area of cost reduction, such
as the expanded use of modular manufacturing, plus a change in mix of styles and
products sold from year to year.

                               Page 7 of 13 pages
<PAGE>   8
           Management's Discussion and Analysis of Financial Condition
                      and Results of Operations - continued


Selling, general and administrative expenses during the quarter amounted to
$16.5 million, an increase of 28.4 percent from the same quarter one year ago.
For the nine months these expenses amounted to $38.9 million, an increase of
19.8 percent from the same period last year. The percentage increases are in
line with the percentage increases in net sales for the periods. Included in
these expenses are those related to the Company's expansion in the French
slipper market, which the Company began during the fourth quarter of 1997.

Net interest expense declined from 1997 to 1998. During the third quarter of
1998, net interest expense amounted to $664 thousand compared with $674 thousand
in the same period of 1997. For the nine months, net interest expense also
declined to $1.2 million in 1998 from $1.3 million in 1997. The decrease in net
interest expense is principally due to the Company's lower average usage of its
Revolver during 1998, than in 1997.

For the third quarter of 1998, the Company earned $6.1 million, or $0.61 per
share, compared with earnings during the same period of 1997 of $5.0 million, or
$0.52 per share. For the nine months, the Company earned $3.7 million in 1998,
or $0.37 per share, compared with earnings in 1997 of $2.1 million, or $0.22 per
share. All per share references in both years represent diluted earnings 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; the effects of competitive products and pricing
pressures; inherent risks of international development, including currency
risks, the implementation of the Euro, economic conditions, regulatory and
cultural difficulties or delays in the Company's development outside the United
States; the Company's ability to improve its processes and business practices to
keep pace with the economic, competitive and technological environment,
including successfully addressing year 2000 issues; 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 8 of 13 pages
<PAGE>   9
                           PART II - OTHER INFORMATION

Item 1.  Legal Proceedings
--------------------------
         On September 10, 1998, the Company filed a lawsuit for patent
         infringement of United States Patent No. 5,790,962 against Domino's
         Pizza, Inc., a Michigan corporation, and Phase Change Laboratories,
         Inc., a Nevada corporation. The case was filed on behalf of both the
         Company and its subsidiary Vesture Corporation in the United States
         District Court for the Middle District of North Carolina. The `962
         patent covers an invention which maintains the desired temperature of
         food and other items using a phase change material. Domino's Pizza,
         Inc. purchases a product which it calls the "Heat Wave" system. The
         product is manufactured by Phase Changes Laboratories, Inc. Study of
         the product indicates that it infringes the `962 patent. The Court has
         granted an extension of time for both defendants to plead. Neither has
         answered or otherwise responded to the Complaint at this time. The
         Company seeks damages, attorney's fees, and an injunction against
         further infringement by both defendants. The Company intends to seek
         lost profits as part of the relief. The case has been assigned Civil
         Action No. 1:98CV00802.

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

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

Item 4.  Submission of Matters to a Vote of Security Holders
------------------------------------------------------------
         (a) through (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 11.

          (b) Reports on Form 8-K: No reports on Form 8-K were filed during the
          quarter ended October 3, 1998.

                               Page 9 of 13 pages
<PAGE>   10
                                   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
November 5, 1998
----------------
      date
                                                /s/ Richard L. Burrell
                                                -----------------------------
                                                Richard L. Burrell
                                                Senior Vice President - Finance
                                                (Principal Financial Officer)
                                                (Duly Authorized Officer)

                               Page 10 of 13 pages
<PAGE>   11
                             R. G. BARRY CORPORATION
                                INDEX TO EXHIBITS

  Exhibit No.                   Description                       Page Number
  -----------                   -----------                       -----------

     27.1        Financial Data Schedule                              12
                 (Period ended October 3, 1998)

     27.2        Financial Data Schedule                              13
                 (Period ended September 27, 1997 Restated)

                               Page 11 of 13 pages