<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    September 27, 1997
                               ------------------------

                                       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 September 27, 1997 - 9,561,210
                                                ------------------------------

                          Index to Exhibits at page 10

                               Page 1 of 11 pages

<PAGE>   2

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

<TABLE>
<CAPTION>
                                                             September 27,      December 28,
                                                             -------------      ------------
                                                                 1997               1996
                                                                 ----               ----
<S>                                                          <C>                 <C>       
ASSETS:
   Cash and cash equivalents                                 $  1,790,000        13,187,000
   Accounts receivable, less allowances                        32,698,000        18,556,000
   Inventory (note 3)                                          48,895,000        28,854,000
   Deferred income taxes (note 4)                               5,055,000         5,055,000
   Prepaid expenses                                             3,428,000         2,027,000
                                                             ------------        ----------
         Total current assets                                  91,866,000        67,679,000
                                                             ------------        ----------

   Property, plant and equipment, at cost                      38,681,000        39,088,000
      Less accumulated depreciation & amortization             24,399,000        25,159,000
                                                             ------------        ----------
         Net property, plant and equipment                     14,282,000        13,929,000
                                                             ------------        ----------

   Goodwill, less accumulated amortization                      4,260,000         4,346,000
   Other assets                                                 3,183,000         3,113,000
                                                             ------------        ----------
                                                             $113,591,000        89,067,000
                                                             ============        ==========

LIABILITIES AND SHAREHOLDERS' EQUITY:
   Current installments of long-term debt
      and capital lease obligations                             2,268,000           125,000
   Short-term notes payable                                    24,000,000              --
   Accounts payable                                             7,010,000         4,170,000
   Accrued expenses                                             4,003,000         9,661,000
                                                             ------------        ----------
      Total current liabilities                                37,281,000        13,956,000
                                                             ------------        ----------

   Accrued retirement costs and other, net                      3,706,000         3,103,000
   Long-term debt and capital lease obligations,
      excluding current installments:
      Note payable                                             12,857,000        15,000,000
      Capital lease obligations                                   265,000           265,000
                                                             ------------        ----------
         Long-term debt and capital lease obligations          13,122,000        15,265,000
                                                             ------------        ----------
            Total liabilities                                  54,109,000        32,324,000
                                                             ------------        ----------

   Shareholders' equity:
      Preferred shares, $1 par value
         Authorized 4,000,000 Class A, and
         1,000,000 Series I Junior Participating
         Class B shares, none issued
      Common shares, $1 par value Authorized
         22,500,000 shares (note 6) (excluding
         treasury shares)                                       9,561,000         9,375,000
      Additional capital in excess of par value                14,479,000        14,071,000
      Retained earnings                                        35,442,000        33,297,000
                                                             ------------        ----------
         Net shareholders' equity                              59,482,000        56,743,000
                                                             ------------        ----------
                                                             $113,591,000        89,067,000
                                                             ============        ==========
</TABLE>

                               Page 2 of 11 pages

<PAGE>   3

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

<TABLE>
<CAPTION>
                                          Thirteen weeks ended           Thirty-nine weeks ended
                                          --------------------           -----------------------
                                      September 27,    September 28,   September 27,   September 28,
                                      -------------    -------------   -------------   -------------
                                          1997             1996            1997            1996
                                          ----             ----            ----            ----
<S>                                    <C>              <C>             <C>             <C>       
Net sales                              $46,361,000      45,161,000      75,835,000      81,196,000
Cost of sales                           24,611,000      25,307,000      38,838,000      44,333,000
                                       -----------      ----------      ----------      ----------
   Gross profit                         21,750,000      19,854,000      36,997,000      36,863,000

Selling, general and
   administrative expenses              12,815,000      11,117,000      32,479,000      30,882,000
                                       -----------      ----------      ----------      ----------
Operating income                         8,935,000       8,737,000       4,518,000       5,981,000

Other income                               111,000         134,000         354,000         341,000

Interest expense                          (693,000)       (862,000)     (1,520,000)     (1,920,000)
Interest income                             19,000          30,000         222,000          94,000
                                       -----------      ----------      ----------      ----------
   Net interest expense                   (674,000)       (832,000)     (1,298,000)     (1,826,000)

Earnings before
   income taxes                          8,372,000       8,039,000       3,574,000       4,496,000
Income tax expense (note 4)              3,348,000       3,219,000       1,429,000       1,803,000
                                       -----------      ----------      ----------      ----------
   Net earnings                        $ 5,024,000       4,820,000       2,145,000       2,693,000
                                       ===========      ==========      ==========      ==========

Earnings per common share (note 5)
      Primary                                $0.52            0.50            0.22            0.27
                                             =====            ====            ====            ====
      Fully diluted                          $0.52            0.50            0.22            0.27
                                             =====            ====            ====            ====

Average number of common
   shares outstanding
      Primary                            9,921,000       9,872,000       9,809,000       9,834,000
                                       ===========      ==========      ==========      ==========
      Fully diluted                      9,971,000       9,872,000       9,844,000       9,834,000
                                       ===========      ==========      ==========      ==========
</TABLE>

                               Page 3 of 11 pages

<PAGE>   4

                    R. G. BARRY CORPORATION AND SUBSIDIARIES
                 CONDENSED CONSOLIDATED STATEMENTS OF CASH FLOW

<TABLE>
<CAPTION>
                                                              Thirty-nine        Thirty-nine
                                                              weeks ended        weeks ended
                                                             September 27,      September 28,
                                                             -------------      -------------
                                                                 1997              1996
                                                                 ----              ----
<S>                                                          <C>                 <C>      
Cash flows from operating activities:
   Net earnings                                              $  2,145,000        2,693,000
   Adjustments to reconcile net earnings to net cash
      used in operating activities:
      Depreciation and amortization of
         property, plant and equipment                          1,322,000        1,203,000
      Amortization of goodwill                                     86,000           87,000
      Net (increase) decrease in:
         Accounts receivable, net                             (14,142,000)     (15,459,000)
         Inventory                                            (20,041,000)     (16,471,000)
         Prepaid expenses                                      (1,401,000)         313,000
         Other                                                    (70,000)         172,000
      Net increase (decrease) in:
         Accounts payable                                       2,840,000       (1,574,000)
         Accrued expenses                                      (5,658,000)      (4,645,000)
         Accrued retirement costs and other                       603,000          343,000
                                                             ------------      -----------
            Net cash used in operating activities             (34,316,000)     (33,338,000)
                                                             ------------      -----------

Cash flows from investing activities:
   Additions to property, plant and equipment, net             (1,675,000)      (1,585,000)
                                                             ------------      -----------

Cash flows from financing activities:
   Proceeds from short-term notes                              24,000,000       33,000,000
   Stock options exercised, net of treasury acquisitions          594,000          406,000
   Repayment of long-term debt and
      capital lease obligations                                         0         (700,000)
                                                             ------------      -----------
         Net cash provided by financing activities             24,594,000       32,706,000
                                                             ------------      -----------

Net decrease in cash                                          (11,397,000)      (2,217,000)
Cash at the beginning of the period                            13,187,000        6,267,000
                                                             ------------      -----------
Cash at the end of the period                                $  1,790,000        4,050,000
                                                             ============      ===========

Supplemental cash flow disclosures:
   Interest paid                                             $  1,705,000        2,066,000
                                                             ============      ===========
   Income taxes paid                                         $  3,770,000        5,618,000
                                                             ============      ===========
</TABLE>


                               Page 4 of 11 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
                    September 27, 1997 and September 28, 1996

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 1997 is a fifty-three week year, with the first three quarters each
     having thirteen weeks and the fourth quarter having fourteen weeks. Fiscal
     1996 was a fifty-two week year, consisting of four quarters each with
     thirteen weeks.

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 September 27, 1997 and September 28, 1996,
     consists of:

<TABLE>
<CAPTION>
                                                                 1997                 1996
                                                                 ----                 ----
<S>                                                           <C>                   <C>
                     Current:
                          U. S. Federal                       $1,204,000            1,503,000
                          State & Local                          225,000              300,000
                                                              ----------            ---------
                               Total                          $1,429,000            1,803,000
                                                              ==========            =========
</TABLE>

     The income tax reflects a combined federal, foreign, state and local
     effective rate of 40 percent for the quarter of both years, as compared to
     the statutory U. S. federal rate of 34 percent in both years.

     Income tax for the periods ended September 27,1997 and September 28, 1996
     differed from the amounts computed by applying the U. S. federal income tax
     rate of 34 percent to pretax earnings as a result of the following:

<TABLE>
<CAPTION>
                                                                 1997                 1996
                                                                 ----                 ----
<S>                                                           <C>                   <C>
                     Computed "expected" tax:
                          U. S. Federal                       $1,215,000            1,530,000
                          Other                                   63,000               75,000
                          State & Local, net of
                            federal income tax                   151,000              198,000
                                                              ----------            ---------
                               Total                          $1,429,000            1,803,000
                                                              ==========            =========
</TABLE>

5.   Net earnings per common share has been computed based on average number of
     common shares outstanding during each period plus, when their effect is
     dilutive, common share equivalents consisting of certain common shares
     subject to stock option and stock purchase plans.

6.   At the Company's Annual Shareholders' Meeting, held on May 16, 1997,
     shareholders approved a proposal to increase the number of authorized
     common shares, $1 par value, of the Company from 15 million to 22.5 million
     shares.

                               Page 5 of 11 pages

<PAGE>   6

                    R. G. BARRY CORPORATION AND SUBSIDIARIES

      ITEM 2 - Management's Discussion and Analysis of Financial Condition
                            and Results of Operations

          "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 environment and the impact of governmental
          regulations, both in the United States and abroad; the effects of
          competitive products and pricing; 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 results may differ from those
          currently anticipated.

Liquidity and Capital Resources
-------------------------------
The Company has ended the third quarter of 1997 with $54.6 million in net
working capital. This compares with $47.2 million at the end of the same quarter
in 1996, and $53.7 million as of the end of fiscal 1996. The increase in net
working capital from the end of the third quarter of 1996 to the end of the
third quarter of 1997, is primarily due to the profit that the Company earned
during fiscal 1996.

The Company's net capital expenditures during the first three quarters of 1997
amounted to $1.7 million, which is nearly the same as the amount of expenditures
in the previous year. Expenditures in both years have been funded out of net
working capital.

A review of the more significant components of net working capital indicates:
o    Accounts receivable decreased slightly at the end of the third quarter of
     1997, to $32.7 million from $33.7 million at the end of the same quarter of
     1996, and increased from $18.6 million at the end of fiscal 1996. While net
     sales for the third quarter of 1997 increased slightly [2.7%], there was a
     slight [3.0%] decline in receivables from third quarter 1996 to 1997. The
     increase in accounts receivable from the end of fiscal 1996 to the end of
     the current quarter, mainly represents a normal seasonal pattern of
     fluctuation in receivables.
o    Inventories ended the third quarter of 1997, at $48.9 million, nearly
     equal to the inventory levels of $48.2 million one year ago, and increased
     from $28.9 million as of the end of fiscal 1996. The increase in
     inventories from the end of fiscal 1996, reflects normal seasonal patterns
     of inventories, as the Company builds seasonal inventories in preparation
     for sales anticipated in the fourth quarter of the year.
o    The Company ended the third quarter of 1997, with $1.8 million in cash and
     $24.0 million in short-term bank loans. This compares with the third
     quarter of 1996, when the Company had $4.1 million in cash and $33 million
     in short-term bank loans. The decrease in short-term bank loans is mainly
     the result of the Company's improved liquidity position, following the year
     end 1996 cash position of $13.2 million. There were no short-term bank
     loans outstanding at the end of fiscal 1996.

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, which the Company believes are 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 though 1999 and contains provisions for periodic extensions upon request
and with the approval of the banks.

                               Page 6 of 11 pages

<PAGE>   7

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

Results of Operations
---------------------
During the third quarter of 1997, net sales amounted to $46.4 million, a 2.7
percent increase from the third quarter of 1996. For the nine months, net sales
amounted to $75.8 million, a 6.6 percent decline from net sales in the first
nine months of 1996. Virtually all of the decline in the first nine months net
sales occurred during the first half of the year. In its 1996 year end Annual
Report to Shareholders, the Company indicated that it expected sales and
earnings for the first half of the year to be lower than in 1996, mainly as a
result of refining its relationship with Corning Consumer Products ("Corning").
During 1997, Corning has outsourced directly the Pyrex(R) Portables(TM) fabric
carriers, which the Company had been providing to Corning. The Company continues
to supply Corning with MICROCORE(R) hot and cold thermal retention elements.
Worldwide net sales of the Company's slipper products grew substantially during
the third quarter compared with last year, and for the nine month period.

The Company had expected net sales and earnings for the third quarter to be
somewhat greater than were actually realized. About $4 million of shipments to
customers that had been anticipated for the third quarter, could not be shipped
before the end of the September, and are expected to be shipped during the
fourth quarter. The Company's production this year was late by about a week,
causing some orders to be held over into October so that they could be shipped
complete to customers.

Gross profit during the third quarter of 1997, amounted to $21.8 million, or
46.9 percent of net sales. This compares with gross profit percent of 44.0
percent in the same quarter of 1996. For the nine months, gross profit percent
also increased to 48.8 percent in 1997 compared with 45.4 percent in 1996. The
increase in gross profit percentages from year to year, is largely due to the
operating efficiencies gained by utilizing modular manufacturing in the
Company's factories. A change in mix of individual styles and products sold from
year to year, also had a positive impact on gross profit percentages.

For the quarter and nine months, total selling, general and administrative
expenses were about 15.3 percent and 5.2 percent higher, respectively, than
similar expenses incurred during the comparable periods of 1996. Had the Company
shipped the additional $4 million to customers in late September as had been
expected, as referred to above, the increase in selling, general and
administrative expenses would have been more in line with the increases in net
sales. In addition, the Company continues to expense its investment in
preparation for its entry into the French slipper market during the latter half
of 1997.

Net interest expense declined from 1996 to 1997. During the third quarter of
1997, net interest expense amounted to $674 thousand compared with $832 thousand
in the same period of 1996. For the nine months, net interest expense also
declined to $1.3 million in 1997 from $1.8 million in 1996. The decrease in net
interest expense is principally due to the Company's lower utilization of its
Revolver to fund short-term seasonal indebtedness during 1997, when compared
with 1996.

During the third quarter of 1997, the Company had net earnings of $5.0 million,
or $0.52 per share, compared with net earnings during the same quarter of 1996
of $4.8 million, or $0.50 per share. For the cumulative nine month period, the
Company earned $2.1 million in 1997, or $0.22 per share, compared with earnings
of $2.7 million in 1996, or $0.27 per share.



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

                               Page 7 of 11 pages

<PAGE>   8

                           PART II - OTHER INFORMATION

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

Item 2.  Changes in Securities and Use of Proceeds
--------------------------------------------------
                  (a) - (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) - (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:  No reports on Form 8-K were filed
                      during the quarter ended September 27, 1997

                               Page 8 of 11 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

November 5, 1997
----------------
      date
                                             /s/ Richard L. Burrell
                                             Richard L. Burrell
                                             Senior Vice President - Finance
                                             (Principal Financial Officer)
                                             (Duly Authorized Officer)

                               Page 9 of 11 pages

<PAGE>   10

                             R. G. BARRY CORPORATION
                                INDEX TO EXHIBITS

<TABLE>
<CAPTION>
  Exhibit No.                    Description                      Page Number
  -----------                    -----------                      -----------
<S>                        <C>                                         <C>
      27                   Financial Data Schedule                     11
</TABLE>

                               Page 10 of 11 pages