<PAGE>   1
================================================================================

                                  UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549

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

                                    FORM 10-Q

                  --------------------------------------------
(Mark One)
   [X]     QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(D) OF THE SECURITIES
                               EXCHANGE ACT OF 1934

                  FOR THE QUARTERLY PERIOD ENDED MAY 31, 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 1-8574



                               UNITED FOODS, INC.
             (Exact name of registrant as specified in its charter)



               DELAWARE                                  74-1264568
       (State of Incorporation)             (I.R.S. Employer Identification No.)

    TEN PICTSWEET DRIVE, BELLS, TN                          38006
(Address of principal executive offices)                  (Zip Code)

       Registrant's telephone number, including area code: (901) 422-7600

      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
                                                  -----      -----

      On June 23, 1998, 2,616,139 shares of Class A Common Stock and 4,193,790
shares of Class B Common Stock of United Foods, Inc. were outstanding.


================================================================================





<PAGE>   2

                                      INDEX

<TABLE>
<CAPTION>
                                                                         PAGE
<S>          <C>                                                         <C>
Part I:      Financial Information:

  Item 1:    Financial Statements:

                Balance Sheets                                             3-4

                Statements of Income                                         5

                Statements of Cash Flows                                   6-7

                Notes to Financial Statements                                8

  Item 2:    Management's Discussion and Analysis of
             Financial Condition and Results of Operations                9-11

Part II:     Other Information and Signatures                               12
</TABLE>








                                       2
<PAGE>   3


                         PART I - FINANCIAL INFORMATION
                          ITEM 1 - FINANCIAL STATEMENTS

                               UNITED FOODS, INC.
                                 BALANCE SHEETS
                             (DOLLARS IN THOUSANDS)

<TABLE>
<CAPTION>
                                                       MAY 31,   FEBRUARY 28,
                                                        1998        1998
                                                     ---------   -----------
                                                     Unaudited
<S>                                                  <C>         <C>
ASSETS

Current Assets:
   Cash                                              $   3,172    $     646
   Accounts Receivable                                  15,359       19,263
   Inventories (Note 3)                                 35,271       37,344
   Prepaid Expenses and Miscellaneous                    3,490        3,935
   Deferred Income Taxes (Note 4)                        1,249        1,249
                                                     ---------    ---------
       Total Current Assets                             58,541       62,437
                                                     ---------    ---------

Property and Equipment:
   Land and Land Improvements                            9,968        9,968
   Buildings and Leasehold Improvements                 21,910       21,399
   Machinery, Equipment and Improvements                96,337       94,870
                                                     ---------    ---------
                                                       128,215      126,237

   Less Accumulated Depreciation                       (76,059)     (74,151)
                                                     ---------    ---------

       Net Property and Equipment                       52,156       52,086
                                                     ---------    ---------

Other Assets                                             1,199        1,361
                                                     ---------    ---------

         Total Assets                                $ 111,896    $ 115,884
                                                     =========    =========

</TABLE>








See accompanying notes to financial statements.



                                       3
<PAGE>   4


                               UNITED FOODS, INC.
                                 BALANCE SHEETS
                             (DOLLARS IN THOUSANDS)


<TABLE>
<CAPTION>
                                                            MAY 31,   FEBRUARY 28,
                                                             1998        1998
                                                          ---------   -----------
                                                          Unaudited
<S>                                                       <C>         <C>
LIABILITIES AND STOCKHOLDERS' EQUITY

Current Liabilities:
   Accounts Payable                                       $  15,017    $  12,191
   Accruals                                                   6,243        6,594
   Income Taxes Payable  (Note 4)                                61           46
   Current Maturities of Long-term Debt                       4,366        4,427
                                                          ---------    ---------
         Total Current Liabilities                           25,687       23,258

Long-term Debt, Less Current Maturities                      35,504       42,168

Deferred Income Taxes (Note 4)                                4,710        4,710
                                                          ---------    ---------

         Total Liabilities                                   65,901       70,136
                                                          ---------    ---------

Stockholders' Equity:
   Common Stock, Class A (Notes 5 and 6)                      2,616        2,616
   Common Stock, Class B, Convertible (Notes 5 and 6)         4,194        4,194
   Additional Paid-in Capital                                 3,993        3,993
   Retained Earnings                                         35,192       34,945
                                                          ---------    ---------


         Total Stockholders' Equity                          45,995       45,748
                                                          ---------    ---------

         Total Liabilities and Stockholders' Equity       $ 111,896    $ 115,884
                                                          =========    =========
</TABLE>









See accompanying notes to financial statements.





                                       4
<PAGE>   5

                               UNITED FOODS, INC.
                        STATEMENTS OF INCOME (UNAUDITED)
                 (DOLLARS IN THOUSANDS EXCEPT PER SHARE AMOUNTS)

<TABLE>
<CAPTION>
                                                              FOR THE THREE
                                                           MONTHS ENDED MAY 31,
                                                       ---------------------------
                                                           1998           1997
                                                       -----------    ------------
<S>                                                    <C>            <C>
Net Sales and Services Less Discounts, Returns and
   and Allowances                                      $    49,934    $     46,963

Costs of Sales and Services (Note 3)                        40,545          38,085
                                                       -----------    ------------

   Gross Profit                                              9,389           8,878

Selling, Administrative and General Expenses                 8,101           7,408
                                                       -----------    ------------

   Operating Income                                          1,288           1,470
                                                       -----------    ------------

Interest Income (Expense) - Net                               (887)           (861)

Miscellaneous Income (Expense) - Net                            --              41
                                                       -----------    ------------

   Total Other Income and (Expense)                           (887)           (820)
                                                       -----------    ------------

   Income Before Taxes on Income                               401             650

Taxes on Income (Note 4)                                       154             250
                                                       -----------    ------------

   Net Income                                          $       247    $        400
                                                       ===========    ============

Weighted Average Common Shares                           6,809,929      10,809,929
                                                       ===========    ============

Basic and Diluted Earnings Per Common Share (Note 6)   $       .04    $        .04
                                                       ===========    ============

Cash Dividends Per Common Share:
   Class A                                                    $-0-            $-0-
   Class B                                                    $-0-            $-0-
</TABLE>



See accompanying notes to financial statements.





                                       5
<PAGE>   6
                               UNITED FOODS, INC.
                      STATEMENTS OF CASH FLOWS (UNAUDITED)
                             (DOLLARS IN THOUSANDS)

<TABLE>
<CAPTION>
                                                           FOR THE THREE
                                                        MONTHS ENDED MAY 31,
                                                          1998       1997
                                                        --------    -------
<S>                                                     <C>         <C>
CASH FLOWS FROM OPERATING ACTIVITIES:
   Net income                                           $    247    $   400
   Adjustments to reconcile net income to net cash
     provided by operations:
     Depreciation and amortization                         1,908      1,852
     Provision for losses on accounts receivable              47         43
     (Gain) on disposal of property and equipment             --        (41)
     Change in assets and liabilities:
       Accounts and notes receivable                       3,857      1,273
       Inventories                                         2,073       (939)
       Prepaid expenses and miscellaneous                    445      1,585
       Other assets                                          162         --
       Accounts payable and accruals                       2,607      2,992
       Income taxes                                           15        (38)
                                                        --------    -------
     Net cash provided by operations                      11,361      7,127
                                                        --------    -------

CASH FLOWS FROM INVESTING ACTIVITIES:
   Capital expenditures                                   (2,110)    (1,215)
   Proceeds from sale of other property and equipment         --         83
                                                        --------    -------
     Net cash used by investing activities                (2,110)    (1,132)
                                                        --------    -------

CASH FLOWS FROM FINANCING ACTIVITIES:
   Proceeds from long-term borrowings                        871        238
   Payments of long-term debt                             (7,596)    (1,130)
                                                        --------    -------
     Net cash used by financing activities                (6,725)      (892)
                                                        --------    -------

NET INCREASE IN CASH FOR THE PERIOD                        2,526      5,103

CASH AND CASH EQUIVALENTS, beginning of period               646      3,772
                                                        --------    -------

CASH AND CASH EQUIVALENTS, end of period                $  3,172    $ 8,875
                                                        ========    =======
</TABLE>

See accompanying notes to financial statements.





                                       6
<PAGE>   7
                               UNITED FOODS, INC.
                      STATEMENTS OF CASH FLOWS (UNAUDITED)
                                   (CONCLUDED)

                             (DOLLARS IN THOUSANDS)

<TABLE>
<CAPTION>
                                                                   FOR THE THREE
                                                                MONTHS ENDED MAY 31,
                                                                --------------------
                                                                   1998      1997
                                                                   ----      ----
<S>                                                                <C>       <C>
SUPPLEMENTAL DISCLOSURES OF CASH FLOW
   INFORMATION:
   Cash paid during the three months for:
     Interest                                                      $888      $871
     Income taxes                                                  $ 13      $142

NON-CASH INVESTING AND FINANCING ACTIVITIES:

   Capital expenditures of $96, $228, $14 and $0 are included
   in accounts payable at May 31, 1998, February 28, 1998,
   May 31, 1997 and February 28, 1997, respectively 
</TABLE>


















See accompanying notes to financial statements.





                                       7
<PAGE>   8





                               UNITED FOODS, INC.
                          NOTES TO FINANCIAL STATEMENTS

1.   The interim financial statements should be read in conjunction with the
     Company's Annual Report on Form 10-K for the year ended February 28, 1998.
     Significant accounting policies and other disclosures normally provided
     have been omitted since such items are disclosed therein.

     In the opinion of the Company, the accompanying unaudited financial
     statements contain all adjustments (consisting of only normal recurring
     accruals) necessary to present fairly its financial position as of May 31,
     1998 and its results of operations and cash flows for the three months
     ended May 31, 1998 and 1997.

2.   The results of operations for the three months ended May 31, 1998 and 1997 
     are not necessarily indicative of the results to be expected for the 
     fiscal year.

3.   Inventories are summarized as follows:

<TABLE>
<CAPTION>
                                            MAY 31, 1998   FEBRUARY 28, 1998
                                            ------------   -----------------
<S>                                         <C>            <C>
      Finished products                      $28,630,000      $31,607,000
      Raw materials                            2,143,000        2,303,000
      Growing crops                            3,438,000        2,644,000
      Merchandise and supplies                 1,060,000          790,000
                                             -----------      -----------

                                             $35,271,000      $37,344,000
                                             ===========      ===========
</TABLE>


     Substantially all of the Company's inventories are valued at the lower of
     cost (first-in, first-out) or market at each fiscal year end. However, due
     to the seasonality of vegetable processing, the gross profit method, at the
     estimated annual rate, is used to determine frozen vegetable cost of goods
     sold in interim financial statements.

4.   Taxes on income consist of the current and deferred taxes required to be
     recognized for the periods presented in accordance with the provisions of
     Statement of Financial Accounting Standards No. 109, "Accounting for Income
     Taxes".

5.   Each Class B common share is convertible into one share of Class A common
     stock at the holder's election. Holders of the Class A common stock are
     entitled to a preference dividend of $.025 per share for any quarter and
     each preceding quarter of the Company's fiscal year before the holders of
     the Class B common stock are entitled to any regular cash dividend. Class A
     shareholders have the right to elect a number of directors that equal at
     least 25% of the members of the board of directors. In addition, on matters
     requiring the classes to vote together, the Class A holders are entitled to
     1/10 vote per share and holders of Class B common stock are entitled to one
     vote per share.

     On May 19, 1997, the Company initiated a cash tender offer for up to one
     million shares of its Class A and Class B Common Stock at a price of $2.50
     per share. On June 17, 1997, the Company amended the cash tender offer by
     extending the Expiration Date to July 3, 1997 and by increasing the number
     of shares it offered to purchase from 1,000,000 shares of its Class A and
     Class B Common Stock to up to 2,500,000 shares of its Class A Common Stock
     and up to 1,500,000 shares of its Class B Common Stock, each at $2.50 per
     share. A total of approximately 2,641,299 shares of Class A Common Stock
     and 1,720,932 shares of Class B Common Stock were validly tendered and not
     withdrawn in response to the offer, as amended. The purchase of shares was
     prorated in accordance with the terms of the offer, as amended, for each
     class of common stock.

6.   Basic and diluted earnings per share of common stock have been computed
     based upon the weighted average number of shares outstanding during the
     three months ended May 31, 1998 and May 31, 1997.






                                       8
<PAGE>   9



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

The following is management's discussion and analysis of certain significant
factors which have affected the Company's financial condition and earnings
during the periods included in the accompanying balance sheets and statements of
income.

SAFE HARBOR STATEMENT UNDER THE PRIVATE SECURITIES LITIGATION REFORM ACT OF 1995

This Quarterly Report on Form 10-Q and other reports and statements issued on
behalf of the Company may include forward-looking information in reliance on the
safe harbor provided by the Private Securities Litigation Reform Act of 1995.
These forward-looking statements are subject to substantial risks and
uncertainties, including those discussed below, and actual results may differ
materially from those contained in any such forward-looking statement. The
review of factors pursuant to the Private Securities Litigation Reform Act of
1995 should not be construed as exhaustive. Further, the Company undertakes no
obligation to update or revise any such forward-looking statements to reflect
subsequent events or circumstances.

The Company's liquidity, capital resources and results of operations may be
affected from time to time by a number of factors and risks, including, but not
limited to: trends in the economy as a whole, which may affect consumer
confidence and consumer demand for the types of food products sold by the
Company; competitive pressures from processors and distributors of fresh, dry,
frozen and canned food products which may affect the nature and viability of the
Company's business strategy; competitive pressures from imported food products;
unpredictable changes in growing conditions inherent in agriculture; other
agricultural risks, including those associated with pesticides, herbicides and
disease control and crop protection efforts; the Company's ability to maintain
and expand the Company's distribution base; the Company's ability to maintain
and improve its plants, equipment and technological systems; changes in the
Company's customer base as the result of competition and/or consolidation of
retail grocery chains; governmental regulation and taxation; availability and
cost of labor employed; changes in industry capacity and production; the
availability, costs and terms of financing, including the risk of rising
interest rates; availability of trade credit and terms with vendors; the
Company's use of financial leverage and the potential impact of such leverage on
the Company's ability to execute its operating strategies; the ability to
maintain gross profit margins; the seasonal nature of the Company's business and
the ability of the Company to predict consumer demand as a whole, as well as
demand for specific items; costs associated with the storage, shipping, handling
and control of inventory; potential adverse publicity for the food industry or
certain of the Company's food products; and the ability of the Company and
significant third parties with whom it does business to effect conversions to
new technological systems, including becoming Year 2000 compliant.

FINANCIAL CONDITION, LIQUIDITY AND CAPITAL RESOURCES

The Company's primary sources of cash are operations and external committed
credit facilities. At May 31, 1998, the Company's revolving credit facilities
totaled $21,000,000, of which $18,000,000 was available. The Company's sources
of liquidity are expected to meet adequately requirements for the upcoming year
and the foreseeable future; however, new financing alternatives are constantly
evaluated to determine their practicality and availability in order to provide
the Company with sufficient and timely funding at the least possible cost. The
$18,000,000 and $3,000,000 revolving credit facilities currently mature in
fiscal 2001. One-year extensions of maturity dates of the revolving credit
facilities will be considered by the lenders annually. If annual extensions are
not granted, the Company will then investigate revolving credit facilities with
other lenders and believes it can replace any current revolving credit facility
within its remaining 24-month term.

In March 1998, the Company entered into a $10,000,000 credit facility for the
acquisition of certain handling equipment, rolling stock, vehicles, trailers and
composting equipment. The facility is evidenced by a master security agreement
with separate loans under the agreement being made for equipment when acquired
and with acquired equipment being secured under the terms of the agreement. The
loans are amortized using respective estimated equipment lives and bear interest
at 160 basis points over the applicable treasury yield. The Company expects to
incur total borrowing of approximately $10,000,000 under the agreement during
fiscal 1999 and had borrowed a total of $642,000 through May 31, 1998.

Operations provided net cash of $11,361,000 during the three months ended May
31, 1998 and $7,127,000 during the same period of the prior year. Changes in
accounts receivable resulted in a cash increase of $3,857,000 during the quarter
as compared with $1,273,000 during the same period of the prior year. The
increase for the current year results primarily from strong sales during
February 1998 that were subsequently collected during the first quarter of the
current fiscal year. Changes 





                                       9

<PAGE>   10

in inventories resulted in a cash increase of $2,073,000 during the quarter as
compared with using cash of $939,000 during the same period of the prior year.
Adverse weather conditions during the first quarter of the current year resulted
in less than expected packs; however, the pack shortfall is expected to be made
up during the remainder of the current fiscal year.

Investing activities used cash of $2,110,000 for the three months ended May 31,
1998 compared with cash used of $1,132,000 during the same period of the prior
year, primarily as the result of increased capital expenditures.

Financing activities used cash of $6,725,000 for the three months ended May 31,
1998 as compared with cash used of $892,000 during the same period of the prior
year. Cash provided by operations was used to reduce borrowings under the
Company's revolving credit agreements during the three months ended May 31,
1998.

On May 19, 1997, the Company initiated a cash tender offer for up to 1,000,000
shares of its Class A and Class B Common Stock at a price of $2.50 per share. On
June 17, 1997, the Company amended the cash tender offer by extending the
Expiration Date to July 3, 1997 and by increasing the number of shares it
offered to purchase from 1,000,000 shares of its Class A and Class B Common
Stock to up to 2,500,000 shares of its Class A Common Stock and up to 1,500,000
shares of its Class B Common Stock, each at a price of $2.50 per share. A total
of approximately 2,641,299 shares of Class A Common Stock and approximately
1,720,932 shares of Class B Common Stock were validly tendered and not withdrawn
in response to the offer, as amended. The purchases of shares were prorated in
accordance with the terms of the offer, as amended, for each class of Common
Stock. The purchase, which totaled approximately $10,168,000, including
expenses, was funded with borrowings from the Company's revolving credit
facilities and available cash.

Working capital at May 31, 1998 was $32,854,000, and was $39,179,000 at February
28, 1998. The decrease results primarily from changes in accounts receivable and
inventories, previously mentioned.

The Company's ratio of debt to equity decreased to 1.43 to 1 at May 31, 1998
from 1.53 to 1 at February 28, 1998, primarily as a result of the decrease in
revolving credit borrowings previously mentioned.

CAPITAL EXPENDITURES

Capital expenditures for fiscal 1999 are estimated to be approximately
$16,600,000, which is approximately $8,500,000 more than depreciation expense
projected for fiscal 1999. Capital expenditures anticipated for fiscal 1999
include outlays to be funded under the terms of the $10,000,000 credit facility,
previously mentioned, as well as for improvements to the Company's plants,
equipment and technological systems. These expenditures are expected to be
funded from operations and the Company's revolving credit facilities. The
Company's capital plan may change from time to time and the actual amount spent
may vary materially from amounts anticipated herein.

RESULTS OF OPERATIONS

OVERVIEW AND TRENDS

The Company's product line is made up of agricultural products which are subject
to the cyclical conditions and risks inherent in the agricultural industry. The
Company bears part of the growing risks and all of the processing and marketing
risks of these agricultural products. Weather abnormalities and excess
inventories sometimes cause substantial reductions in the annual volume of
product processed in the Company's facilities. When this happens, the unit cost
of that year's production will increase substantially, resulting in reduced
profit margins for one or more years. On the other hand, when bumper crops occur
unit costs will decrease but selling prices will, in general, be depressed.

The Company is faced with very strong competition in the marketplace from large
brand name competitors, private regional U.S. growers and processors, and
privately-owned Mexican and Canadian growers and processors. These competitive
pressures, coupled with low overall growth, have led to weak market pricing, and
a substantial increase in trade spending required for the Company to maintain
its market position. These factors have adversely impacted earnings in certain
prior periods and, as a result, certain discretionary repair and maintenance
projects were deferred to later periods. The Company anticipates that these
competitive conditions will continue.

The Company believes in order to address the intense competition within its
industry, it must improve its operational efficiency, lower its costs, improve
its customer service and provide value-added services to its customers.
Accordingly, the 



                                       10
<PAGE>   11


Company intends to continue to invest in maintaining and expanding its
distribution base and to make substantial expenditures to maintain and improve
its plants, equipment and technological systems. The Company believes these
expenditures are necessary to keep its business competitive and will fund such
spending during periods when earnings are available. As a result, the Company
expects that its future earnings, if any, may be decreased from historical
levels.

In addition to general inflation and the growing, processing and marketing risks
described above, the Company is facing the significant costs associated with
governmental regulation, the loss of land and water available for agriculture in
California and the increasing competition due to worldwide facilitation of
trade. As a result of these factors, the Company's earnings are subject to
fluctuations and will continue to be so in the future.

The effect on the Company's operations and its ability to withstand the costs of
evolving healthcare, OSHA, EPA, taxation and other governmental regulations is
unknown.

REVENUES

Net sales and service revenue increased $2,971,000 (6.3%); sales volume
increased 2.1% and the average per pound selling price increased 5.8% for the
quarter ended May 31, 1998, as compared with the same period of the prior year.
Sales to other food processors decreased $1,081,000 (27.3%); excluding the
effect of the decrease in sales to other food processors, sales volume and the
average per pound selling price increased 9.6% and 1.1%, respectively, for the
quarter ended May 31, 1998, as compared with the same prior year period. Sales
allowances increased $1,155,000 (13.7%), primarily as a result of the 9.6% sales
volume increase previously mentioned, as well as competitive market conditions
and the Company's efforts in maintaining its market position.

COST OF SALES AND SERVICES

Gross profit increased $511,000 (5.8%) for the quarter ended May 31, 1998, as
compared with the same period of the prior year and the gross margin decreased
to 18.8% from 18.9%. The increase in gross profit results primarily from margin
realized on additional sales volumes, previously mentioned. The gross profit
method, at the estimated annual gross profit rate is used to determine frozen
vegetable cost of goods sold in interim financial statements (See Note 3 - Notes
to Financial Statements). Cost of sales and services increased $2,460,000 (6.5%)
for the three months ended May 31, 1998, as compared with the same period of the
prior year, primarily as the result of the sales volume increases previously
mentioned.

SELLING, ADMINISTRATIVE AND GENERAL EXPENSES

Selling, general and administrative expenses increased $693,000 (9.4%) for the
quarter compared with the same period of the prior year. Storage expense
increased $444,000 (21.1%) for the quarter as compared with the same period of
the prior year, primarily as the result of repairs to the Company's cold storage
facilities. Other selling, general and administrative expenses increased
$249,000 (4.7%), primarily as the result of label design costs.

INTEREST EXPENSE

Interest expense - net increased $26,000 (3.0%) for the quarter ended May 31,
1998, as compared with the prior year, primarily as the result of changes in
average borrowings and cash and short term investments.

TAXES ON INCOME

Taxes on income for the three months ended May 31, 1998 and 1997 consist of
current and deferred taxes provided at the estimated effective federal and state
tax rates expected to be recognized for the respective periods. (See Note 4 -
Notes to Financial Statements.)





                                       11
<PAGE>   12



                           PART II - OTHER INFORMATION


Item 6.    Exhibits and Reports on Form 8-K

                (a)    Exhibits
                        
                       27  Financial Data Schedule (SEC Use Only)

                (b)    Reports on Form 8-K - There were no reports on Form 8-K 
                       filed during the three months ended May 31, 1998.











                                   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.




                                           UNITED FOODS, INC.



Date:  June 26, 1998                  By:  s/ Carl W. Gruenewald, II
       -------------                       -------------------------
                                           Carl W. Gruenewald, II
                                           Senior Vice President,
                                           Chief Financial Officer & Treasurer







                                       12