<PAGE>   1
                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549

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

                                 F O R M  10-Q

For the Quarter Ended April 4, 1998               Commission File Number 1-5315

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

                  S P R I N G S  I N D U S T R I E S,  I N C.
             (Exact name of registrant as specified in its charter)

            SOUTH CAROLINA                                      57-0252730
     (State or other jurisdiction of                        (I.R.S. Employer
      incorporation or organization)                       Identification No.)


205 North White Street
Fort Mill, South Carolina                                         29715
(Address of principal executive offices)                       (Zip Code)

               Registrant's telephone number, including area code:
                                 (803) 547-1500

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


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 at least the past 90 days.

Yes   X    No
    -----     -----

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


As of May 8, 1998, there were 11,804,379 shares of Class A Common Stock and
7,270,921 shares of Class B Common Stock of Springs Industries, Inc.
outstanding.

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


There are 16 pages in the sequentially numbered, manually signed original of
this report.

                                  Page 1 of 16
                       The Index to Exhibits is on Page 15

<PAGE>   2


                         TABLE OF CONTENTS TO FORM 10-Q


<TABLE>
<CAPTION>
PART I - FINANCIAL INFORMATION


ITEM                                                                 PAGE
----                                                                 ----
<S>     <C>                                                          <C>
1.      FINANCIAL STATEMENTS                                           3

2.      MANAGEMENT'S DISCUSSION AND ANALYSIS OF                        9
          FINANCIAL CONDITION AND RESULTS OF OPERATIONS


PART II - OTHER INFORMATION


4.      SUBMISSION OF MATTERS TO A VOTE                                12
          OF SECURITY HOLDERS

6.      EXHIBITS                                                       13


SIGNATURES                                                             14

EXHIBIT INDEX                                                          15
</TABLE>


                                      -2-
<PAGE>   3


                                     PART I
                          ITEM I - FINANCIAL STATEMENTS




SPRINGS INDUSTRIES, INC.
Consolidated Statement of Operations
and Retained Earnings
(In thousands except per share data)
(Unaudited)

<TABLE>
<CAPTION>
                                                        THIRTEEN WEEKS ENDED
                                                      -----------------------
                                                       APRIL 4,     MARCH 29,
                                                         1998          1997
                                                      ---------     ---------
<S>                                                   <C>            <C>
OPERATIONS
  Net sales ......................................    $ 556,736      $ 543,009
  Cost and expenses:
    Cost of goods sold ...........................      455,059        446,757
    Selling, general and
      administrative expenses ....................       75,001         70,753
    Restructuring and
      realignment expenses .......................       24,850          2,763
    Year 2000 expenses ...........................        1,420            279
    Interest expense .............................        5,554          4,521
    Other income .................................         (144)          (149)
                                                      ---------      ---------
      Total ......................................      561,740        524,924
                                                      ---------      ---------

  Income (loss) before income taxes ..............       (5,004)        18,085

  Income tax provision (benefit) .................       (1,905)         6,874
                                                      ---------      ---------

    Net income (loss) ............................    $  (3,099)     $  11,211
                                                      =========      =========

  Earnings per common share - basic:
    Net income (loss) ............................    $    (.16)     $     .56
                                                      =========      =========

  Earnings per common share - diluted:
     Net Income (loss) ...........................    $    (.16)     $     .54
                                                      =========      =========

  Cash dividends declared:
    Class A shares ...............................    $     .33      $     .33
                                                      =========      =========
    Class B shares ...............................    $     .30      $     .30
                                                      =========      =========

RETAINED EARNINGS
  Retained earnings at beginning
    of period ....................................    $ 701,354      $ 675,533
  Net income (loss) ..............................       (3,099)        11,211
  Repurchase of Class A common stock .............      (29,059)             -
  Cash dividends declared ........................       (6,188)        (6,435)
                                                      ---------      ---------

  Retained earnings at end of period .............    $ 663,008      $ 680,309
                                                      =========      =========
</TABLE>


See Notes to Condensed Consolidated Financial Statements.


                                       -3-
<PAGE>   4


SPRINGS INDUSTRIES, INC.
Condensed Consolidated Balance Sheet
(In thousands except share data)
(Unaudited)

<TABLE>
<CAPTION>
                                                   APRIL 4,       JANUARY 3,
                                                     1998            1998
                                                 -----------     -----------
<S>                                              <C>             <C>        
ASSETS
Current assets:
  Cash and cash equivalents .................    $       399     $       373
  Accounts receivable .......................        347,697         317,702
  Inventories, net ..........................        457,066         420,295
  Other .....................................         52,296          48,309
                                                 -----------     -----------
    Total current assets ....................        857,458         786,679
                                                 -----------     -----------

Property, plant and equipment ...............      1,355,824       1,340,154
  Accumulated depreciation ..................       (816,055)       (799,623)
                                                 -----------     -----------
    Property, plant and equipment, net ......        539,769         540,531
                                                 -----------     -----------
Other assets ................................         81,963          81,533
                                                 -----------     -----------
    Total ...................................    $ 1,479,190     $ 1,408,743
                                                 ===========     ===========

LIABILITIES AND SHAREOWNERS' EQUITY
Current liabilities:
  Short-term borrowings .....................    $    61,950     $     7,450
  Current maturities of long-term debt ......         17,793          14,452
  Accounts payable ..........................         97,586          92,135
  Accrued restructuring costs ...............         15,890           4,647
  Other accrued liabilities .................         99,666         121,409
                                                 -----------     -----------
    Total current liabilities ...............        292,885         240,093
                                                 -----------     -----------

Noncurrent liabilities:
  Long-term debt ............................        220,429         164,287
  Accrued benefits and deferred
   compensation .............................        175,339         173,681
  Other .....................................         25,501          26,084
                                                 -----------     -----------
    Total noncurrent liabilities ............        421,269         364,052
                                                 -----------     -----------

Shareowners' equity:
  Class A common stock- $.25 par value
    (12,062,582 and 12,601,757 shares
    issued in 1998 and 1997, respectively) ..          3,016           3,150
  Class B common stock- $.25 par value
    (7,270,921 shares issued and
    outstanding in 1998 and 1997) ...........          1,818           1,818
  Additional paid-in capital ................        107,748         108,684
  Retained earnings .........................        663,008         701,354
  Cost of Class A shares in treasury
    (100,203 and 101,091 shares in 1998
    and 1997, respectively) .................         (2,263)         (2,276)
  Currency translation adjustment and other .         (8,291)         (8,132)
                                                 -----------     -----------
    Total shareowners' equity ...............        765,036         804,598
                                                 -----------     -----------
    Total ...................................    $ 1,479,190     $ 1,408,743
                                                 ===========     ===========
</TABLE>


See Notes to Condensed Consolidated Financial Statements.


                                      -4-
<PAGE>   5


SPRINGS INDUSTRIES, INC.
Condensed Consolidated Statement of Cash Flows
(In thousands)
(Unaudited)

<TABLE>
<CAPTION>
                                                                  THIRTEEN WEEKS ENDED
                                                                ------------------------
                                                                APRIL 4,       MARCH 29,
                                                                  1998           1997
                                                                --------       ---------
<S>                                                             <C>            <C>
Operating activities:
  Net income (loss) ...................................         $ (3,099)      $ 11,211
  Adjustments to reconcile net income (loss) to
   net cash used by operating activities:
   Depreciation and amortization ......................           23,266         22,721
   Provision for restructuring costs ..................           23,049              -
   Changes in operating assets and liabilities,
    net of effects of business acquisitions ...........          (77,608)       (52,778)
   Other, net .........................................           (5,274)        (4,799)
                                                                --------       --------
      Net cash used by operating activities ...........          (39,666)       (23,645)
                                                                --------       --------

Investing activities:
  Purchases of property, plant and
    equipment .........................................          (33,299)       (15,465)
  Business acquisitions ...............................                -         (6,400)
  Principal collected on notes receivable .............            2,002            600
  Notes receivable funded .............................                -         (8,000)
  Proceeds from sales of assets .......................              311            378
                                                                --------       --------
     Net cash used by investing activities ............          (30,986)       (28,887)
                                                                --------       --------

Financing activities:
  Proceeds (repayments) from short-term
    borrowings, net ...................................           54,500         36,800
  Proceeds from long-term borrowings ..................           60,000              -
  Repayments of long-term debt ........................             (517)          (557)
  Repurchase of Class A shares ........................          (32,367)             -
  Proceeds from exercise of stock options .............            1,600              -
  Cash dividends paid .................................          (12,538)       (12,859)
                                                                --------       --------
      Net cash provided by financing activities .......           70,678         23,384
                                                                --------       --------
Increase (decrease) in cash and cash
 equivalents ..........................................         $     26       $(29,148)
                                                                ========       ========
</TABLE>


See Notes to Condensed Consolidated Financial Statements.


                                      -5-

<PAGE>   6


              NOTES TO CONDENSED CONSOLIDATED FINANCIAL STATEMENTS

1.       Significant Accounting Policies:

         The accompanying condensed consolidated financial statements should be
         read in conjunction with the financial statements presented in the
         Springs Industries, Inc. ("Springs" or the "Company") 1997 Annual
         Report on Form 10-K.

         In the opinion of the management of Springs, these unaudited condensed
         consolidated financial statements contain all adjustments of a normal
         recurring nature necessary for their fair presentation. The results for
         interim periods reflect estimates for certain items which can be
         definitively determined only on an annual basis. These items include
         the valuation of a substantial portion of inventories on a LIFO cost
         basis and the provision for income taxes. These interim financial
         statements reflect applicable portions of the estimated annual amounts
         for such items.

         The results of operations for interim periods are not necessarily
         indicative of operating results to be expected for the remainder of the
         year.

2.       Inventories:

         Inventories are summarized as follows (in thousands):

<TABLE>
<CAPTION>
                                                        April 4,      Jan. 3,
                                                         1998           1998
                                                       ---------      ---------
       <S>                                             <C>           <C>
       Standard cost (which approximates
       average cost) or average cost:
        Finished goods...........................      $ 313,345      $ 280,316
        In process...............................        205,651        199,600
        Raw materials and supplies...............         59,924         59,381
                                                       ---------      ---------
                                                         578,920        539,297
       Less LIFO reserve.........................       (121,854)      (119,002)
                                                       ---------      ---------

        Total....................................      $ 457,066      $ 420,295
                                                       =========      =========
</TABLE>

3.       Restructuring and Realignment Costs:

         During the first quarter of 1998, the Company adopted a plan to close
         the Company's Rock Hill Printing and Finishing Plant. The phase-down of
         the facility is expected to begin in May of 1998 and to take
         approximately five months. A pretax charge of $23.0 million was
         recorded in the first quarter of 1998, including $11.3 million for
         write-offs of plant and equipment, $4.0 million for severance arising
         from the elimination of approximately 480 positions, and $7.7 million
         for certain other expenses associated with the closing of the facility.
         No cash expenditures were recorded against the accruals in the first
         quarter. In connection with the closing of this plant, the Company
         expects to incur approximately $8.0 million for equipment relocation
         and other realignment expenses which do not qualify as "exit costs."


                                      -6-

<PAGE>   7


         In the second quarter of 1996, the Company adopted a plan to
         consolidate and realign its fabric manufacturing operations. A pretax
         restructuring charge of $30.4 million was recorded in the second
         quarter of 1996 which included a $16.3 million write-off of plant and
         equipment, a $6.6 million accrual for anticipated severance arising
         from the elimination of approximately 850 positions, and a $7.5 million
         accrual for certain other anticipated expenses associated with the
         plan. Through April 4, 1998, the Company has recorded cash expenditures
         of approximately $4.2 million against the severance accrual and $5.5
         million against the accrual for certain other expenses associated with
         the plan. In addition, the Company has incurred expenses of $16.7
         million, including $1.8 million in 1998, for equipment relocation and
         other realignment expenses related to the plan.


4.       Other:

         The Company presently expects to spend approximately $15 million during
         1998 and 1999 to modify its computer information systems to ensure the
         proper processing of transactions relating to Year 2000 and beyond.
         This "Year 2000 Computer Problem" creates risk for the Company from
         unforeseen problems in its own computer systems and those of third
         parties with whom the Company conducts business transactions. Year
         2000-related failures of the Company's and/or third parties' computer
         systems could have a material impact on the Company's ability to
         conduct its business. Management currently believes that Company
         information systems affected by the Year 2000 issues have been
         identified and that its implementation plans will ensure compliance for
         its systems by the Year 2000. The pretax amount expensed in the first
         quarter of 1998 in connection with these efforts was $1.4 million,
         compared to $0.3 million in the first quarter of 1997.

         In 1997, the Financial Accounting Standards Board issued Statement No.
         130, "Reporting Comprehensive Income," which was required to be adopted
         for fiscal years beginning after December 15, 1997. This Statement
         establishes standards for reporting and display of comprehensive
         income. Comprehensive income (loss) was ($3.2) million for the first
         quarter of 1998 and $11.3 million for the first quarter of 1997. The
         difference between net income and comprehensive income was accumulated
         translation adjustments of $(99) thousand for the first quarter of 1998
         and $54 thousand for the first quarter of 1997.
         

5.       Legal and Environmental:

         As disclosed in the 1997 Annual Report on Form 10-K, Springs is
         involved in certain administrative proceedings alleging violations of
         environmental laws and regulations, including proceedings under the
         Comprehensive Environmental Response, Compensation, and Liability Act.
         In connection with these proceedings, the Company has accrued an amount
         which represents management's best estimate of Springs' probable
         liability.


                                      -7-

<PAGE>   8

         Springs is also involved in various other legal proceedings and claims
         incidental to its business. Springs is protecting its interests in all
         such proceedings.

         In the opinion of management, based on the advice of counsel, the
         likelihood that the resolution of the above matters would have a
         material adverse impact on either the financial condition or the future
         results of operations of Springs is remote.


                                      -8-

<PAGE>   9


                 ITEM 2. - MANAGEMENT'S DISCUSSION AND ANALYSIS

GENERAL

During the first quarter of 1998 the Company announced a $67.0 million plan to
modernize and expand its towel manufacturing. Nearly $40.0 million is expected
to be spent in Hartwell, Georgia, to build a new weaving plant and to modernize
a yarn manufacturing facility, nearly doubling the capacity of that plant. Over
$26.0 million is expected to be spent to modernize terry manufacturing
facilities in Griffin, Georgia. The plan is expected to be completed in
approximately 15 months.

In addition, the Company adopted a plan in the first quarter of 1998 to close
the Company's Rock Hill Printing and Finishing Plant. The phase-down of the
facility is expected to begin in May of 1998 and to take approximately five
months. A pretax charge of $23.0 million was recorded in the first quarter of
1998, including $11.3 million for write-offs of plant and equipment, $4.0
million for severance arising from the elimination of approximately 480
positions, and $7.7 million for certain other expenses associated with the
closing of the facility. No cash expenditures were recorded against the accruals
in the first quarter. In connection with the closing of this plant, the Company
expects to incur approximately $8.0 million for equipment relocation and other
realignment expenses which do not qualify as "exit costs."

RESULTS OF OPERATIONS

Sales

Net sales for the first quarter of 1998 were $556.7 million, up about 3 percent
from the first quarter of 1997. Springs' 1997 first-quarter results reflected
its participation in the largest retail rollouts of new home furnishings
programs in industry history. Nevertheless, the home furnishings segment, in
1998, generated record first-quarter sales, up 2 percent from last year. The
specialty fabrics segment's first-quarter sales increased by 4 percent compared
to 1997.

Earnings

The Company reported a net loss of $3.1 million, or $.16 per diluted share, for
the first quarter of 1998, compared to net income of $11.2 million, or $.54 per
diluted share, for 1997. The loss was caused by three unusual items: the $23.0
million pretax charge associated with the planned closing of the Rock Hill
Printing and Finishing Plant, realignment expenses associated with the
restructuring of fabric manufacturing operations, and charges incurred for Year
2000 modifications to information systems. Without these unusual items, net
income for the first quarter of 1998 would have been $13.2 million, or $.66 per
diluted share, compared to $13.1 million, or $0.64 per diluted share, for 1997.
In the home furnishings segment, profits were slightly below last year. Profits
for the specialty fabrics segment were significantly below last year due to the
restructuring charge recorded in the first quarter of 1998. Excluding the
restructuring charge and Year 2000 expenses, profits for the specialty fabrics
segment showed improvement compared to last year.


                                      -9-

<PAGE>   10


CAPITAL RESOURCES AND LIQUIDITY

Increases in accounts receivable and inventory resulted in a first-quarter
increase in short-term borrowings. Proceeds from long-term debt were used to
finance purchases of equipment and Class A shares during the first quarter of
1998. The Company expects capital expenditures for 1998 to approximate $150
million. The focus of the Company's investments will be on new state-of-the-art
manufacturing, distribution and information technology.

In October of 1997, the Company's Board of Directors approved the purchase of up
to 2 million shares of the Company's Class A common stock. The Company had
repurchased 988,500 shares through the first quarter of 1998.

The Company presently expects to spend approximately $15 million during 1998 and
1999 to modify its computer information systems to ensure the proper processing
of transactions relating to Year 2000 and beyond. This "Year 2000 Computer
Problem" creates risk for the Company from unforeseen problems in its own
computer systems and those of third parties with whom the Company conducts
business transactions. Year 2000-related failures of the Company's and/or third
parties' computer systems could have a material impact on the Company's ability
to conduct its business. Management currently believes that Company information
systems affected by the Year 2000 issues have been identified and that its
implementation plans will ensure compliance for its systems by the Year 2000.
The pretax amount expensed in the first quarter of 1998 in connection with these
efforts was $1.4 million, compared to $0.3 million in the first quarter of 1997.

RESTRUCTURING AND REALIGNMENT

During the second quarter of 1996, the Company adopted a plan to consolidate and
realign its fabric manufacturing operations. A pretax restructuring charge of
$30.4 million was recorded in the second quarter of 1996 which included a $16.3
million write-off of plant and equipment, a $6.6 million accrual for anticipated
severance arising from the elimination of approximately 850 positions, and a
$7.5 million accrual for certain other anticipated expenses associated with the
plan. Through April 4, 1998, the Company has recorded cash expenditures of
approximately $4.2 million against the severance accrual and $5.5 million
against the accrual for certain other expenses associated with the plan. In
addition, the Company has incurred expenses of $16.7 million, including $1.8
million in 1998, for equipment relocation and other realignment expenses related
to the plan. Over the next 8 months, Springs plans to incur expenses of
approximately $5.2 million for equipment relocation and other realignment costs
related to the plan which do not qualify as "exit costs."

As noted above, the Company adopted a plan in the first quarter of 1998 to close
the Rock Hill Printing and Finishing Plant. A pretax charge of $23.0 million was
recorded during the first quarter of 1998.


                                      -10-

<PAGE>   11


FORWARD LOOKING INFORMATION

This Form 10-Q report contains forward-looking statements that reflect
management's expectations, estimates, projections, and assumptions of future
performance and economic conditions. Words such as "expects," "anticipates,"
"plans," "believes," "estimates," and variations of such words and similar
expressions are intended to identify such forward-looking statements which
include but are not limited to projections of expenditures, cash flows, and
operating performance. The Company cautions investors that any forward-looking
statement is subject to risks and uncertainties that may cause actual results to
vary significantly from those projected, stated, or implied by the
forward-looking statement. Factors that could cause actual results to differ are
discussed in the Company's most recently filed 10-K.


                                      -11-

<PAGE>   12


                          PART II - OTHER INFORMATION

          ITEM 4 - SUBMISSION OF MATTERS TO A VOTE OF SECURITY HOLDERS

         (a) The annual meeting of the security holders of the Company was held
on April 20, 1998.

         (b) During the annual meeting, the security holders of the Company
elected the following directors to hold office until the next annual meeting of
the security holders and until a successor is duly elected and qualified:

                  John F. Akers                      Aldo Papone
                  Crandall Close Bowles              Donald S. Perkins
                  John L. Clendenin                  Robin B. Smith
                  Leroy S. Close                     Sherwood H. Smith, Jr.
                  Charles W. Coker                   Stewart Turley
                  John H. McArthur

         (c)
<TABLE>
<CAPTION>
   Description of Matter Voted Upon         For       Against or    Abstentions
                                                      Withheld
<S>                                      <C>                        <C>
(i)
Annual election of
directors:
John F. Akers                            38,405,246                    285,334
Crandall Close Bowles                    38,622,779                     67,801
John L. Clendenin                        38,640,341                     50,239
Leroy S. Close                           38,662,789                     67,791
Charles W. Coker                         38,642,147                     48,433
John H. McArthur                         38,640,535                     50,045
Aldo Papone                              38,640,645                     49,935
Donald S. Perkins                        38,641,209                     49,371
Robin B. Smith                           38,640,163                     50,417
Sherwood H. Smith, Jr.                   38,639,992                     50,588
Stewart Turley                           38,642,455                     48,125


(ii)
Ratification of the                      38,659,236    19,585           11,759
appointment of Deloitte & 
Touche as the Company's
auditors
</TABLE>


         (d)  N/A


                                      -12-

<PAGE>   13


                                ITEM 6 - EXHIBITS


The following exhibits are filed as part of this report:

         (27)     Financial Data Schedule


                                      -13-

<PAGE>   14


                                   SIGNATURES


Pursuant to the requirements of Securities Exchange Act of 1934, Springs
Industries, Inc. has duly caused this Report to be signed on its behalf by the
undersigned thereunto duly authorized.

                                    SPRINGS INDUSTRIES, INC.



                                    By:  /s/ James F. Zahrn
                                         ---------------------------------
                                         James F. Zahrn
                                         Executive Vice President and
                                         Chief Financial Officer
                                         (Duly Authorized Officer and
                                         Principal Financial Officer)




DATED:  May 19, 1998


                                      -14-
<PAGE>   15


                                  EXHIBIT INDEX


Item                                                               
----                                                         

(27)               Financial Data Schedule (for SEC purposes)


                                      -15-