<PAGE>
 
                      SECURITIES AND EXCHANGE COMMISSION

                            Washington, D. C.  20549

                                  FORM 10-QSB
 
[X] Quarterly Report under Section 13 or 15(d) 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:                 1-3753
                        --------------------------------------------------------
                                        
                         UNITED PARK CITY MINES COMPANY
--------------------------------------------------------------------------------
       (exact name of small business issuer as specified in its charter)


                Delaware                                    87-0219807
-------------------------------------------------    ---------------------------
      (State or other jurisdiction of                    (I.R.S. Employer
       incorporation or organization.)                   Identification No.)


       P. O. Box 1450, Park City, Utah                         84060
-------------------------------------------------    ---------------------------
(Address of principal executive offices)                     (Zip Code)

                                (435) 649-8011
--------------------------------------------------------------------------------
                          (Issuer's telephone number)


Check whether the issuer (1) filed all reports required to be filed by Section
13 or 15(d) of the Exchange Act during the past 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    .
     ---     ---  

                    (APPLICABLE ONLY TO CORPORATE ISSUERS)

State the number of shares outstanding of each of the issuer's classes of common
equity, as of the latest practicable date:   3,249,411, as of May 1, 1999.

Transitional Small Business Disclosure Format (check one):  Yes    ; No  X .
                                                                ---     ---
<PAGE>
                                                                    Form 10-QSB
                                                 United Park City Mines Company
                                                                 March 31, 1999
                                                                         Page 2

                         PART I - FINANCIAL INFORMATION
                UNITED PARK CITY MINES COMPANY AND SUBSIDIARIES
                           CONSOLIDATED BALANCE SHEET
                                  (Unaudited)

<TABLE> 
<CAPTION> 
                                                                                                      March 31,
                                                                                                        1999 
                                                                                                --------------------
<S>                                                                                             <C> 
ASSETS:
Cash and cash equivalents............................................................                 $2,869,786
Accounts receivable..................................................................                    186,815
Prepaid expenses.....................................................................                    151,509
Inventories..........................................................................                    175,802
Deferred income taxes................................................................                    270,068
Other................................................................................                     21,100
                                                                                                --------------------
                                                                                                       3,675,080
                                                                                                --------------------
Real Estate:
  Hidden Meadows development.........................................................                    858,207
  Deer Crest development.............................................................                    503,590
  Deferred development costs.........................................................                  2,259,179
                                                                                                --------------------
                                                                                                       3,620,976
                                                                                                --------------------
Property and Equipment:
  Mine shaft, buildings and equipment................................................                  4,091,420
  Mine tour attraction...............................................................                  4,952,941
  Construction-in-progress...........................................................                    241,962
  Resort facilities..................................................................                     58,077
  Less accumulated depreciation......................................................                 (5,028,553)
                                                                                                --------------------
                                                                                                       4,315,847

  Land less accumulated depletion of $1,062,190......................................                 12,982,458
  Water rights.......................................................................                    400,000
                                                                                                --------------------
                                                                                                      17,698,305
                                                                                                --------------------
Total assets.........................................................................                $24,994,361
                                                                                                ====================
</TABLE> 

  The accompanying notes are an integral part of the consolidated financial 
                                  statements.
<PAGE>
                                                                    Form 10-QSB
                                                 United Park City Mines Company
                                                                 March 31, 1999
                                                                         Page 3

 
                UNITED PARK CITY MINES COMPANY AND SUBSIDIARIES
                          CONSOLIDATED BALANCE SHEET
                                  (Unaudited)


<TABLE>
<CAPTION>
                                                                                                     March 31,
                                                                                                       1999
                                                                                                -----------------
LIABILITIES AND STOCKHOLDERS' EQUITY:
<S>                                                                                    <C>
Accounts payable.....................................................................                  $  357,985
Accrued liabilities..................................................................                     708,334
                                                                                                -----------------
  Total liabilities..................................................................                   1,066,319
                                                                                                -----------------

Stockholders' equity:
  Capital stock, $.01 par value:
    Authorized:  3,750,000 shares
    Issued:  3,249,411 shares.........................................................                    32,494
  Capital in excess of par value.....................................................                 41,982,640
  Accumulated deficit................................................................                (17,903,308)
                                                                                                -----------------
                                                                                                      24,111,826
  Less cost of treasury stock - 1,294 shares.........................................                   (183,784)
                                                                                                -----------------
  Total stockholders' equity.........................................................                 23,928,042
                                                                                                ----------------- 
Total liabilities and stockholders' equity...........................................               $ 24,994,361
                                                                                                =================
</TABLE>

  The accompanying notes are an integral part of the consolidated financial 
                                  statements.
<PAGE>
                                                                     Form 10-QSB
                                                  United Park City Mines Company
                                                                  March 31, 1999
                                                                          Page 4

 
                UNITED PARK CITY MINES COMPANY AND SUBSIDIARIES
                     CONSOLIDATED STATEMENT OF OPERATIONS
                                  (Unaudited)


<TABLE>
<CAPTION>
                                                                                  For Three Months Ended
                                                                        --------------------------------------   
                                                                            March 31,             March 31,
                                                                               1999                 1998
                                                                        -------------------  -----------------  
<S>                                                                   <C>                     <C>
Revenues:
 Lot sales..........................................................                                $  705,000
 Mine tour attraction...............................................             $  225,242            276,477
 Interest...........................................................                 37,196             34,899
 Royalties and rentals..............................................                 88,399             93,250
 Contract services..................................................                 56,103             47,925
 Other..............................................................                 16,111              2,949
                                                                        -------------------  -----------------  
                                                                                    423,051          1,160,500
                                                                        -------------------  -----------------   
 
Expenses:
 Cost of lot sales and selling expenses.............................                 32,655            417,568
 Mine tour attraction...............................................                327,905            355,201
 General and administrative costs...................................                232,705            234,984
 Mine maintenance and administrative costs..........................                377,194            263,260
 Contract services costs............................................                 47,137             40,545
 Depreciation.......................................................                128,814            130,273
 Interest...........................................................                                    14,074
                                                                        -------------------  -----------------   
                                                                                  1,146,410          1,455,905
                                                                        -------------------  -----------------   
Loss before income tax..............................................               (723,359)          (295,405)
 
 Income tax expense.................................................                      0                  0
                                                                        -------------------  -----------------   
Net loss............................................................             $ (723,359)       $  (295,405)
                                                                        ===================  =================    
Net loss per share:
Basic and diluted...................................................                 $(0.22)       $     (0.09)
                                                                        ===================  =================     
Weighted average number of shares outstanding:
Basic and diluted...................................................              3,249,411          3,138,508
                                                                        ===================  =================     

</TABLE>

  The accompanying notes are an integral part of the consolidated financial 
                                  statements.
<PAGE>
                                                                     Form 10-QSB
                                                  United Park City Mines Company
                                                                  March 31, 1999
                                                                          Page 5


 
                UNITED PARK CITY MINES COMPANY AND SUBSIDIARIES
                     CONSOLIDATED STATEMENT OF CASH FLOWS
                                  (Unaudited)


<TABLE>
<CAPTION>
                                                                                  For Three Months Ended
                                                                        -------------------------------------------
                                                                            March 31,                March 31,
                                                                              1999                     1998
                                                                        -------------------   ---------------------
<S>                                                                   <C>                     <C>
Cash flows from operating activities:
  Net loss..........................................................            $  (723,359)             $ (295,405)
                                                                        -------------------   ---------------------
  Adjustments to reconcile net loss to net
  cash used by operating activities:
     Depreciation...................................................                128,814                 130,273
     Increase (decrease) from changes in:
      Accounts receivable...........................................               (131,404)                (76,969)
      Prepaid expenses and inventories..............................                 29,670                  40,957
      Hidden Meadows development costs..............................                                        331,944
      Deferred development costs-other..............................               (284,037)               (202,809)
      Accounts payable and accrued liabilities......................                (10,398)                (33,383)
      Contracts payable.............................................                                        (65,000)
                                                                        -------------------   ---------------------
          Total adjustments.........................................               (267,355)                125,013
                                                                        -------------------   ---------------------
Net cash used by operating activities...............................               (990,714)               (170,392)
                                                                        -------------------   --------------------- 
Cash flows from investing activities:
  Construction-in-progress..........................................                 (5,994)                 (5,244)
  Capital expenditures..............................................                (23,980)                 (7,862)
                                                                        -------------------   ---------------------
Net cash used by investing activities...............................                (29,974)                (13,106)
                                                                        -------------------   --------------------- 
Cash flows from financing activities:
  Costs related to issuing stock for land...........................                                        (36,893)
                                                                        -------------------   ---------------------
Net cash used by financing activities...............................                                        (36,893)
                                                                        -------------------   --------------------- 
Net decrease in cash and cash equivalents...........................             (1,020,688)               (220,391)
Cash and cash equivalents-beginning of period.......................              3,890,474               3,360,878
                                                                        -------------------   ---------------------
Cash and cash equivalents-end of period.............................            $ 2,869,786              $3,140,487
                                                                        ===================   =====================

</TABLE>

  The accompanying notes are an integral part of the consolidated financial 
                                  statements.
<PAGE>
                                                                    Form 10-QSB
                                                 United Park City Mines Company
                                                                 March 31, 1999
                                                                         Page 6


UNITED PARK CITY MINES COMPANY AND SUBSIDIARIES
SELECTED NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)
------------------------------------------------------------------------------- 

NOTE 1  CONDENSED FINANCIAL STATEMENTS

A.  Disclosure

Certain information and footnote disclosures normally included in financial
statements prepared in accordance with generally accepted accounting principles
have been condensed or omitted.  It is suggested that these financial statements
be read in conjunction with the 1998 Annual Report on Form 10-KSB of United Park
City Mines Company (hereinafter "United Park" or "the Company" or "the
Registrant").

B.  Management's Representation

The consolidated balance sheet as of March 31, 1999 and the consolidated
statements of operations and cash flows for the three month periods ended March
31, 1999 and March 31, 1998 have been prepared by the Registrant, without audit.
In the opinion of management, all adjustments (which include only normal
recurring adjustments) necessary to present fairly the financial position,
results of operations, and cash flows as of March 31, 1999 and for all periods
presented have been made.

NOTE 2  IMPACT OF RECENTLY ISSUED ACCOUNTING STANDARDS

The Company has reviewed all recently issued Accounting Standards and does not
believe that any of the Standards will have a material effect upon the financial
statements of the Company.

NOTE 3  LAND ACQUISITION

The Company acquired the assets of New Quincy Mining Company and Lucky Bill
Mining Company during the first quarter of 1998.  The acquired assets consisted
of approximately 212 acres of land within the area of the Company's Flagstaff
Mountain Resort. The Company exchanged 203,700 shares of its capital stock for
the land.

NOTE 4  INDUSTRY SEGMENTS

During 1998, the Company adopted Statement of Financial Accounting Standard No.
131, "Disclosures about Segments of an Enterprise and Related Information."  The
Company's reportable segments are strategic business units that offer different
products and services.  They are managed separately because each business
requires different technology and marketing strategies.  The Company is
organized into the following industry segments and management accounts for
revenues and expenses from these activities separately and evaluates each of the
following segments based upon performance: Mine Maintenance, Real Estate and
Mine Tour.  The segment data here presented does not include intersegment
revenues or charges for corporate overhead costs.

<TABLE>
<CAPTION>
March 31, 1999:                       Mine Maint.   Real Estate   Mine Tour      Other        Total
------------------------------------ -------------  -----------  -----------  -----------  ------------
<S>                                   <C>           <C>          <C>          <C>          <C>
Revenue.............................    $  67,469   $    88,060  $  225,242   $   42,280   $   423,051
Operating income (loss)/1/..........     (231,018)       13,101    (213,613)    (291,829)     (723,359)
Identifiable assets.................      806,303    16,440,463   3,962,998    3,784,597    24,994,361
 
March 31, 1998:                       Mine Maint.   Real Estate   Mine Tour      Other         Total
------------------------------------ -------------  -----------  -----------  -----------  ------------
Revenue.............................    $  48,175   $   799,000  $  278,323   $   35,002   $ 1,160,500
Operating income (loss)/1/..........     (231,104)      323,254    (185,002)    (202,553)     (295,405)
Identifiable assets.................      864,824    15,396,411   4,252,303    4,234,603    24,748,141
/1/Earnings before taxes
</TABLE>
<PAGE>
                                                                    Form 10-QSB
                                                 United Park City Mines Company
                                                                 March 31, 1999
                                                                         Page 7 

MANAGEMENT'S DISCUSSION AND ANALYSIS
OF FINANCIAL CONDITION AND RESULTS OF OPERATIONS
-------------------------------------------------------------------------------

This Form 10-QSB may contain trend information and forward-looking statements
that involve risks and uncertainties.  The actual results of operations of the
Company could differ materially from the Company's historical results of
operations and those discussed in such forward-looking statements as a result of
certain factors set forth in this section and elsewhere in this Form 10-QSB,
including information incorporated by reference.

Liquidity and Capital Resources

Real Estate
-----------

The Company's wholly owned subsidiary Blue Ledge Corporation (hereinafter "Blue
Ledge") sold lots in the Hidden Meadows subdivision during the first three
months of 1998, and, consequently, Blue Ledge recognized a profit of $287,432 on
gross sales of $705,000.  The cash proceeds from these lot sales were used to
fund a portion of the Company's operations.  Blue Ledge did not sell any lots in
the Hidden Meadows subdivision during the first quarter of 1999.

During the first quarter of 1998, the Company acquired the assets of New Quincy
Mining Company (hereinafter "New Quincy") and Lucky Bill Mining Company
(hereinafter "Lucky Bill").  The assets of New Quincy and Lucky Bill consisted
of approximately 212 acres of land within the area of the Company's Flagstaff
Mountain Resort development.  This acquisition of land should greatly enhance
the Company's development opportunities with that project.   The Company
exchanged 203,700 shares of its capital stock for the land (reference is made to
the Prospectus which is a part of the Form S-3, Amendment No. 1, dated April 8,
1998, filed by the Company with the Securities and Exchange Commission for a
more complete description of the transaction).

The Company continues to pursue the necessary approvals for its master planned
real estate development projects known as Flagstaff Mountain Resort and Bonanza
Mountain Resort with Park City Municipal Corporation ("Park City") and Wasatch
County. The Company expects Park City and Wasatch County to act upon the
Company's request for approval of the projects during 1999.

Cash Flow Analysis
------------------

The Company's cash balance decreased $1,020,688 during the first three months of
1999, leaving a cash balance of $2,869,786 as of March 31, 1999.  During the
first quarter of 1999, the Company's operating activities used cash of $990,714
as compared to cash used during the first quarter of 1998 of $170,392.  The
Company will use a portion of the March 31, 1999 cash balance along with a
portion of the proceeds from future real estate sales by Blue Ledge and net
revenues from the Company's wholly owned subsidiary Park City Silver Mine
Adventure, Inc. (hereinafter "Silver Mine Adventure") to fund its future
operations. The Company believes that its existing capital resources and cash
flows from operations will be sufficient to meet its anticipated operating
requirements for 1999.

Year 2000 Compliance
--------------------

The Company is currently completing the remedies, corrections and updates to its
information systems (computers and software) which correct or minimize the
Company's risk with regard to the Year 2000 issue.  The costs associated with
updating and correcting its computers and software are not expected to exceed
$35,000 and the Company expects to be compliant by June 30, 1999 (reference is
made to the Company's 1998 Form 10-KSB filed with the Securities and Exchange
Commission for a complete description of the Company's Year 2000 compliance
program).
<PAGE>
                                                                     Form 10-QSB
                                                  United Park City Mines Company
                                                                  March 31, 1999
                                                                          Page 8


MANAGEMENT'S DISCUSSION AND ANALYSIS
OF FINANCIAL CONDITION AND RESULTS OF OPERATIONS
--------------------------------------------------------------------------------
 
Results of Operations

1999 Compared with 1998
-----------------------

During the first three months of 1999, the Silver Mine Adventure generated
revenues of $225,242 and incurred $327,905 in expenses as compared to revenues
of $276,477 and expenses of $355,201 for the same period in 1998. This 19%
decrease in revenues is primarily the result of a change in operating the Silver
Mine Adventure from seven (7) days a week during the first quarter of 1998 to
five (5) days a week for the same period in 1999.  While the Silver Mine
Adventure has not achieved profitability to date, the Company expects its
continued implementation of cost efficiencies and increased promotions during
the summer tourist season will continue to contribute to the Company's revenues.

Blue Ledge sold lots in the Hidden Meadows subdivision for a profit of $287,432
or 41% of the gross sales price during the first quarter of 1998.  Blue Ledge
did not sell any lots in the Hidden Meadows subdivision during the first quarter
of 1999.  However, Blue Ledge incurred expenses associated with holding,
managing and marketing the unsold lots of $32,655 during the first quarter of
1999.

The Company's interest income increased 7% during the first three months of
1999, when compared with the first three months of 1998.  The increase in
interest income is due to larger cash balances available for investment during
the first quarter of 1999.

The Company received $56,103 for contract services performed during the first
quarter of 1999 as compared to $47,925 for the same period in 1998. The increase
of 17% is the result of an increase in the amount of tunnel repair work being
performed for a third party.

Other revenues increased $13,162 during the three month period ended March 31,
1999 when compared to the same period in 1998.  The increase is primarily the
result of the Company's receipt of additional revenues from the rental of water.

Increased labor, material and legal costs resulted in an increase in mine
maintenance and administrative costs of approximately 43% during the first
quarter of 1999 when compared with the same period in 1998.  The increase in
such costs is due to the Company's allocation of personnel and resources to its
tunnel maintenance activities and its efforts to improve the surface estate of
its mountainous properties.
<PAGE>
                                                                    Form 10-QSB
                                                 United Park City Mines Company
                                                                 March 31, 1999
                                                                         Page 9

 
                                   PART II.
                               OTHER INFORMATION


ITEM 6.   EXHIBITS AND REPORTS ON FORM 8-K

(a)  Exhibits filed with this Form 10-QSB:

Exhibit 27 - Financial Data Schedule for electronic filers is filed with this
Form 10-QSB pursuant to Item 601(c) of Regulation S-B.

(b)  Reports on Form 8-K filed during the period covered by this Form 10-QSB:

No reports on Form 8-K were filed during the period covered by this Form 10-QSB.
<PAGE>
                                                                     Form 10-QSB
                                                  United Park City Mines Company
                                                                  March 31, 1999
                                                                         Page 10

 
                                  SIGNATURES

In accordance with the requirements of the Exchange Act, the Registrant caused
this report to be signed on its behalf by the undersigned, thereunto duly
authorized.


                         United Park City Mines Company
            ------------------------------------------------------
                                 (Registrant)



<TABLE>
<CAPTION>
                       s/ Edwin L. Osika, Jr.                                   s/ Michael R. Salmond
        ---------------------------------------------------     --------------------------------------------------------   
        <S>                                                     <C> 
                      Edwin L. Osika, Jr.                                        Michael R. Salmond
                    Executive Vice President,                                        Controller
                    Secretary, and Treasurer                               (Principal Accounting Officer)
               (Principal Financial Officer and
                   Duly Authorized Officer)
 
Date:  May 10, 1999
       ------------
</TABLE>