<PAGE>
 
                                   Form 10-Q

                      SECURITIES AND EXCHANGE COMMISSION
                            WASHINGTON, D.C. 20549

               QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(d)
[X]                 OF THE SECURITIES EXCHANGE ACT OF 1934
                 For the quarterly period ended March 31, 1999

                                      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 1-5666
                         -----------------------------

                            UNION TANK CAR COMPANY
            (Exact name of registrant as specified in its charter)

             Delaware                                       36-3104688
             --------                                       ----------
  (State or other jurisdiction of                        (I.R.S. Employer
   incorporation or organization)                     Identification Number)

              225 West Washington Street, Chicago, Illinois 60606
              ---------------------------------------------------
                   (Address of principal executive offices)

      Registrant's telephone number, including area code: (312) 372-9500

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
                                      ---     --- 
      
There is no voting stock held by non-affiliates of the registrant. This report
is being filed by the registrant as a result of undertakings made pursuant to
Section 15(d) of the Securities Exchange Act of 1934.

Included in this filing are 10 pages, sequentially numbered in the bottom center
of each page.

                                      -1-
<PAGE>
 
                    UNION TANK CAR COMPANY AND SUBSIDIARIES
                                   FORM 10-Q
                                     INDEX
                                                                            Page
                                                                            ----
Part I.  Financial Information                  

         Item 1. 

                Condensed consolidated statement of income - 
                 three months ended March 31, 1999 and 1998                   3 

                Condensed consolidated balance sheet -
                 March 31, 1999 and December 31, 1998                         4

                Condensed consolidated statement of cash flows - 
                 three months ended March 31, 1999 and 1998                   5

                Notes to condensed consolidated financial statements         6-7

         Item 2.

                Management's Discussion and Analysis            
                 of Financial Condition and Results of Operations             8

         Item 3.

                Disclosures About Market Risk                                 9


Part II. Other Information

         Item 1.

                Legal Proceedings                                             9

         Item 6.

                Exhibits and Reports on Form 8-K                              9

Signatures                                                                   10 

                                      -2-


<PAGE>
 
                         PART I. FINANCIAL INFORMATION

ITEM 1. FINANCIAL STATEMENTS

                    UNION TANK CAR COMPANY AND SUBSIDIARIES
                  CONDENSED CONSOLIDATED STATEMENT OF INCOME
                            (Dollars in Thousands)
                                  (Unaudited)
 
<TABLE> 
<CAPTION> 

                                                        Three Months Ended
                                                             March 31,
                                                        -------------------
                                                          1999       1998 
                                                        --------   -------- 
<S>                                                     <C>        <C> 
Revenues
  Services (leasing and other)                          $153,319   $142,237  
  Net sales                                               73,187     53,377  
                                                        --------   --------  

                                                         226,506    195,614  
Other income                                               4,440     10,323  
                                                        --------   --------  

                                                         230,946    205,937  
Costs and expenses                                                           
  Cost of services                                        88,162     78,288  
  Cost of sales                                           60,937     44,517  
  General and administrative                              17,736     14,812  
  Interest                                                17,045     18,615  
                                                        --------   --------  

                                                         183,880    156,232  
                                                        --------   --------  

Income before income taxes                                47,066     49,705  
                                                                             
Provision for income taxes                                                   
  Current                                                 13,316     19,222  
  Deferred                                                 5,299         60  
                                                        --------   --------   

                                                          18,615     19,282  
                                                        --------   --------   

Net income                                              $ 28,451   $ 30,423  
                                                        ========   ========
</TABLE> 

           See notes to condensed consolidated financial statements.

                                      -3-
<PAGE>
 



                    UNION TANK CAR COMPANY AND SUBSIDIARIES
                     CONDENSED CONSOLIDATED BALANCE SHEET
                            (Dollars in Thousands)
                                  (Unaudited)

<TABLE>
<CAPTION>

                                                            March 31,                December 31,
                                                              1999                       1998
                                                          -----------                ------------
Assets
------
<S>                                                       <C>                        <C>
Cash and cash equivalents                                 $   58,930                 $   58,423
Accounts receivable, primarily due within one year            92,330                     82,729
Inventories                                                   86,244                     90,123
Prepaid expenses and deferred charges                         10,377                     11,411
Advances to parent company,
  principally at LIBOR plus 1%                               120,864                    130,940
Railcar lease fleet, net                                   1,599,541                  1,575,014
Fixed assets, net                                            176,976                    177,055
Investment in aircraft direct financing lease                 32,956                     32,629
Other assets                                                  61,286                     53,851
                                                          ----------                 ----------
     Total assets                                         $2,239,504                 $2,212,175
                                                          ==========                 ==========

Liabilities, Deferred Items and Stockholder's Equity
----------------------------------------------------

Accounts payable                                          $   21,477                 $   20,082
Accrued liabilities                                          227,581                    252,897
Borrowed debt, including $47,302 due within
  one year ($46,951 at December 31, 1998)                    904,870                    868,421
                                                          ----------                 ----------
                                                           1,153,928                  1,141,400

Deferred income taxes and investment tax credits             444,043                    437,693


Stockholder's equity
  Common stock and additional capital                        113,035                    113,035
  Retained earnings                                          528,498                    520,047
                                                          ----------                 ----------
    Total stockholder's equity                               641,533                    633,082
                                                          ----------                 ----------
    Total liabilities, deferred items and
        stockholder's equity                              $2,239,504                 $2,212,175
                                                          ==========                 ==========
</TABLE>

           See notes to condensed consolidated financial statements.

                                     -4-




<PAGE>
 
                    UNION TANK CAR COMPANY AND SUBSIDIARIES
                CONDENSED CONSOLIDATED STATEMENT OF CASH FLOWS
                            (Dollars in Thousands)
                                  (Unaudited)

<TABLE>
<CAPTION>
                                                             Three Months Ended
                                                                  March 31,
                                                             ------------------
                                                               1999      1998   
                                                             --------  --------
<S>                                                          <C>       <C>
Cash flows from operating activities:                                          
  Net income                                                 $ 28,451  $ 30,423
  Adjustments to reconcile net income to net cash                              
   provided by operating activities:                                            
    Depreciation and amortization                              32,113    30,059 
    Deferred taxes                                              5,299        60 
    Gain on disposition of railcars and other fixed assets       (946)     (603)
    Other non-cash income and expenses                            449       314 
    Changes in assets and liabilities:                                          
      Accounts receivable                                     (10,152)    2,586 
      Inventories                                               3,387    (3,850)
      Prepaid expenses and deferred charges                     1,016       603 
      Accounts payable and accrued expenses                   (24,577)   (8,903)
                                                             --------  -------- 
Net cash provided by operating activities                      35,040    50,689 
                                                                               
Cash flows from investing activities:                  
  Construction and purchase of railcars and other fixed 
   assets                                                     (65,801)  (60,375)
  Decrease (increase) in advance to parent                      7,720    (5,687)
  (Increase) in other assets                                   (8,722)      --
  Proceeds from disposals of railcars and other fixed assets    2,549     1,585 
                                                             --------  -------- 
Net cash used in investing activities                         (64,254)  (64,477)
                                                                               
Cash flows from financing activities:                                           
  Proceeds from issuance of borrowed debt                      45,000       --  
  Proceeds from sale-leaseback transaction                     13,200    88,570 
  Principal payments of borrowed debt                          (9,248)  (52,953)
  Cash dividend                                               (20,000)  (21,000)
                                                             --------  ---------
Net cash provided by financing activities                      28,952    14,617 
                                                                                
Effect of exchange rates on cash and cash equivalents             769       849 
                                                             --------  -------- 
Net increase in cash and cash equivalents                         507     1,678 
                                                                                
Cash and cash equivalents at beginning of year                 58,423    99,709 
                                                             --------  -------- 
Cash and cash equivalents at end of period                   $ 58,930  $101,387 
                                                             ========  ======== 
Cash paid during the period for:                                               
  Interest (net of amount capitalized)                       $ 19,958  $ 19,199 
  Income taxes                                                 17,955    19,646
</TABLE>

           See notes to condensed consolidated financial statements.

                                      -5-
<PAGE>
 
                    UNION TANK CAR COMPANY AND SUBSIDIARIES
             NOTES TO CONDENSED CONSOLIDATED FINANCIAL STATEMENTS
                            (Dollars in Thousands)
                                  (Unaudited)

1.   UNION TANK CAR COMPANY (the "Company") is a wholly-owned subsidiary of
     Marmon Industrial LLC ("Marmon Industrial"). Marmon Industrial is a wholly-
     owned subsidiary of Marmon Holdings, Inc. ("Marmon Holdings"),
     substantially all of the stock of which is owned, directly or indirectly,
     by trusts for the benefit of certain members of the Pritzker family. As
     used herein, "Pritzker family" refers to the lineal descendants of Nicholas
     J. Pritzker, deceased.

2.   The accompanying unaudited condensed consolidated financial statements
     include all adjustments, consisting of normal recurring accruals, which the
     Company considers necessary for a fair presentation. These interim
     financial statements do not include all disclosures normally provided in
     annual financial statements. Accordingly, they should be read in
     conjunction with the consolidated financial statements and notes thereto in
     the Company's 1998 Annual Report on Form 10-K.

     The 1999 interim results presented herein are not necessarily indicative of
     the results of operations for the full year 1999.

3.   As more fully described in the Company's 1998 Annual Report on Form 10-K,
     under an arrangement with Marmon Industrial, the Company is included in the
     consolidated federal income tax return of Marmon Holdings. As a member of a
     consolidated federal income tax group, the Company is contingently liable
     for the federal income taxes of the other members of the group.

4.   The Company and its subsidiaries have been named as defendants in a number
     of lawsuits, and certain claims are pending. The Company has accrued what
     it reasonably expects to pay in resolution of these matters and, in the
     opinion of management, their ultimate resolution will not have a material
     effect on the Company's consolidated financial position or results of
     operations.

5.   Foreign currency translation adjustments and transaction gains and losses
     are assumed by the Company's parent. For the three months ended March 31,
     1999 and 1998, Marmon Industrial absorbed losses of $252 and $266,
     respectively.

6.   The Company's Canadian subsidiaries periodically enter into foreign
     currency forward contracts to hedge against U.S. dollar exposures. Foreign
     currency forward contracts, all with initial maturities of less than one
     year, amounted to $3,365 at December 31, 1998. There were no forward
     exchange contracts outstanding at March 31, 1999.

                                      -6-
<PAGE>


 
7.   Segment Information

<TABLE> 
<CAPTION> 
                                                                                                    Consolidated  
                                                                 Railcar          All Other            Totals     
                                                                 -------          ---------            ------     
                                                                            (Dollars in Millions)                  
<S>                                                             <C>               <C>               <C>    
     Three months ended March 31, 1999
     --------------------------------- 
     Revenues from external customers                           $ 177.7            $ 48.8              $ 226.5
     Income before income taxes                                    48.4              (1.3)                47.1
                                                                                      
     Three months ended March 31, 1998                                                
     ---------------------------------                                                
     Revenues from external customers                           $ 162.8            $ 32.8              $ 195.6
     Income before income taxes                                    45.3               4.4                 49.7 
</TABLE> 

8.   Summarized Financial Information of Procor Limited

     Summarized consolidated financial information for the Company's wholly-
     owned subsidiary, Procor Limited, in thousands of U.S. dollars, is as
     follows:

<TABLE> 
<CAPTION> 
                                                                                 March 31,                 December 31,
                                                                                   1999                        1998        
                                                                                -----------                ------------   
<S>                                                                             <C>                        <C> 
     Balance Sheet:
       Railcar lease fleet, net                                                 $ 163,952                   $ 165,270
       All other assets                                                           170,370                     170,214
       Borrowed debt                                                               94,210                      94,409
       All other liabilities                                                      103,335                     109,431
 

                                                                                           Three Months Ended        
                                                                                               March 31,              
                                                                                -------------------------------------- 
                                                                                   1999                        1998
                                                                                -----------                 ----------    
     Statement of Income:                              
       Services and net sales                                                   $  29,913                   $  26,654
       Gross profit                                                                 8,400                       9,201
       Net income                                                                   3,303                       3,554
</TABLE> 

9.   In January 1999, the Company entered into a sale-leaseback transaction with
     a financial institution pursuant to which it sold and leased back an
     aggregate of $13,200 in railcars. The Company has an option to purchase all
     of the railcars at a fixed purchase price on January 31, 2019.

10.  In March 1999, the Company issued $45,000 principal amount of unsecured
     Medium-Term Notes. The notes bear interest at rates between 6.00% and 6.35%
     with maturity ranging from three to nine years. Interest will be payable
     semiannually on March 1 and September 1, commencing September 1, 1999.

11.  In April 1999, the Company issued $25,000 principal amount of unsecured
     Medium-Term Notes. The notes bear interest at 5.91% with maturity on May 1,
     2002. Interest will be payable semiannually on March 1 and September 1,
     commencing September 1, 1999.

                                      -7-
<PAGE>
 
ITEM 2.  MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION
         AND RESULTS OF OPERATIONS

Results of Operations
---------------------
1st Quarter 1999 versus 1998
----------------------------
Service revenues increased $11.1 million primarily due to the effect of railcars
added to the lease fleet.

Sales revenues increased $19.8 million primarily due to increased sales of
railcars and sales of mobile railcar moving vehicles, a business which was
acquired in the fourth quarter of 1998.

Other income decreased $5.9 million primarily due to the 1998 sale of certain
rights retained as a condition of the May 1996 sale of a storage facility used
in liquefied petroleum gas storage operations.

Financial Condition 
-------------------
1999 versus 1998
----------------
Operating activities provided $35.0 million of cash. These funds, along with the
issuance of borrowed debt and the sale-leaseback transaction, were used to
provide financing for railcar additions, service borrowed debt obligations, and
pay a dividend to the Company's stockholder.

Management expects future cash to be provided from operating activities, long-
term financings and collection of funds previously advanced to parent will be
adequate to provide for the continued expansion of the Company's business and
enable it to meet its debt service obligations.

Year 2000
---------
Because of the potential importance to the Company of Year 2000 questions, the
Company has established a Year 2000 program to determine the Company's state of
readiness and the costs it anticipates it will have to incur in light of any
possible problems and to remediate any problems discovered. The Company's Year
2000 assessment indicated that the Company's accounting, invoicing, general
business and fleet management systems would be affected by Year 2000 problems.
The Company has begun the necessary corrective work on its coding, invoicing,
general business and fleet management systems that would be affected by Year
2000 problems. The work is approximately 95% complete. The Company's timetable
calls for this work to be substantially completed by May 31, 1999, with testing
of the completed systems to be done by July 31, 1999.

The Company does not believe its main products (i.e., tank cars and other rail
cars) have any material Year 2000 exposures. Similarly, no material problems
have been identified in connection with the Company's production machinery and
equipment.

The Company is using both in-house resources and outside consultants to
implement the necessary changes required by its Year 2000 program. The total
cost of the program is estimated to be $4.8 million, which will be funded from
operating cash flow. Through March 31, 1999, the Company has spent approximately
$3.3 million related to its Year 2000 program, of which $3.1 million has been
expensed and $0.2 million has been capitalized. Of the remaining amount,
approximately $0.3 million is expected to be capitalized with the balance being
expensed.

For further discussion of the Company's Year 2000 program and risks related
thereto, see "Management's Discussion and Analysis of Financial Condition and
Results of Operations" in the Company's Annual Report on Form 10-K for the year
ended December 31, 1998.

                                      -8-
<PAGE>
 
ITEM 3. DISCLOSURES ABOUT MARKET RISK

At March 31, 1999, there has been no significant change to the Company's
exposure to market risk since December 31, 1998.


                          PART II. OTHER INFORMATION

ITEM 1. Legal Proceedings

        Reference is made to "Business - Environmental Matters" in the Company's
        Annual Report on Form 10-K for the year ended December 31, 1998 for a
        description of certain environmental matters.

ITEM 6. Exhibits and Reports on Form 8-K

     b. No report on Form 8-K was filed during the quarter ended March 31, 1999.


                                      -9-
<PAGE>
 
                                  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.


                                        UNION TANK CAR COMPANY

                                        REGISTRANT

Dated: May 7,1999                       /s/ R.C. Gluth
                                        -----------------------------
                                            R.C. Gluth
                                        Executive Vice President,
                                         Director and Treasurer
                                         (principal financial officer
                                          and principal accounting 
                                          officer)


                                     -10-