<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
     JUNE 30, 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:                          1-3753
                        --------------------------------------------------------


                        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)


                                (801) 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 August 13, 1998.

Transitional Small Business Disclosure Format (check one):  Yes    ;  No  X .
                                                                ---      --- 
<PAGE>
 
                                                                     Form 10-QSB
                                                  United Park City Mines Company
                                                                   June 30, 1998
                                                                          Page 2


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


                                                               June 30, 
                                                                 1998   
                                                             ----------- 
ASSETS:                                                                 
Cash and cash equivalents.................................   $ 2,516,396
Accounts receivable.......................................       159,581
Prepaid expenses..........................................       115,378
Material and supplies inventories.........................       193,753
Deferred income taxes.....................................       475,202
Other.....................................................        11,100
                                                             ----------- 
                                                               3,471,410
                                                             ----------- 
Real Estate:                                                            
  Hidden Meadows development costs........................     1,209,240
  Deferred development costs - other......................     1,580,527
                                                             -----------
                                                               2,789,767
                                                             ----------- 
Property and Equipment:                                                 
  Mine shaft, buildings, and equipment....................     4,091,263
  Mine tour attraction....................................     4,852,617
  Construction-in-progress................................       240,587
  Resort facilities.......................................        58,077
  Less accumulated depreciation...........................    (4,680,856)
                                                             ----------- 
                                                               4,561,688
                                                                        
Land less accumulated depletion of $1,062,190.............    12,795,003
Water rights..............................................       400,000
                                                             ----------- 
                                                              17,756,691
                                                             ----------- 

Total assets..............................................   $24,017,868
                                                             =========== 

  The accompanying notes are an integral part of the consolidated financial 
                                  statements.
<PAGE>
 
                                                                     Form 10-QSB
                                                  United Park City Mines Company
                                                                   June 30, 1998
                                                                          Page 3



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

                                                               June 30,
                                                                 1998
                                                             ------------ 
LIABILITIES AND STOCKHOLDERS' EQUITY:
Accounts payable..........................................   $    270,974
Accrued liabilities.......................................        536,550
                                                             ------------ 
  Total liabilities.......................................        807,524
                                                             ------------ 

Stockholders' equity:
  Common stock, $.01 par value:
    Authorized: 3,750,000 shares
    Issued: 3,249,411 shares..............................         32,494
  Capital in excess of par value..........................     41,984,147
  Accumulated deficit.....................................    (18,622,513)
                                                             ------------ 
                                                               23,394,128

  Less cost of treasury stock - 1,294 shares (at cost)....       (183,784)
                                                             ------------ 

  Total stockholders' equity..............................     23,210,344
                                                             ------------ 

Total liabilities and stockholders' equity................   $ 24,017,868
                                                             ============

  The accompanying notes are an integral part of the consolidated financial 
                                  statements.
<PAGE>
 
                                                                     Form 10-QSB
                                                  United Park City Mines Company
                                                                   June 30, 1998
                                                                          Page 4

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


<TABLE>
<CAPTION>
                                             For Three Months Ended     For Six Months Ended
                                            -----------------------   ------------------------ 
                                             June 30,     June 30,     June 30,     June 30,
                                               1998         1997         1998         1997
                                            ----------   ----------   ----------   -----------
<S>                                         <C>          <C>          <C>          <C>
Revenues:
 Lot sales................................  $  385,000   $  670,000   $1,090,000   $   855,000
 Mine tour attraction.....................     355,296      340,448      631,773       633,099
 Interest.................................      36,755         (278)      71,654         5,932
 Royalties and rentals....................      48,755       82,885      142,005       181,510
 Contract services........................      14,741       16,837       62,666        60,553
 Other....................................       3,135       36,923        6,084        41,496
                                            ----------   ----------   ----------   -----------
                                               843,682    1,146,815    2,004,182     1,777,590
                                            ----------   ----------   ----------   -----------
 
Expenses:
 Cost of lot sales and selling expense....     186,328      395,316      603,896       509,692
 Mine tour attraction.....................     390,020      510,219      745,221       891,051
 General and administrative costs.........     279,519      332,927      514,503       597,679
 Mine maintenance and administrative                                                         
   costs..................................     347,895      180,778      611,155       459,617
 Contract services costs..................      (3,263)       5,724       37,282        42,154
 Depreciation.............................     129,814      123,640      260,087       247,471
 Interest.................................      11,533       17,121       25,607        45,433
                                            ----------   ----------   ----------   -----------
                                             1,341,846    1,565,725    2,797,751     2,793,097
                                            ----------   ----------   ----------   -----------
 
Loss before income tax....................  $ (498,164)  $ (418,910)  $ (793,569)  $(1,015,507)
 
 Income tax benefit.......................           0            0            0             0
                                            ----------   ----------   ----------   ----------- 

Net loss..................................  $ (498,164)  $ (418,910)    (793,569)  $(1,015,507)
                                            ==========   ==========   ==========   =========== 

Basic and diluted loss per share..........  $    (0.16)  $    (0.15)  $    (0.25)  $     (0.37)
                                            ==========   ==========   ==========   =========== 
 
Weighted average number of shares
  outstanding.............................   3,194,266    2,701,819    3,194,266     2,701,682
                                            ==========   ==========   ==========   ===========  
</TABLE>

  The accompanying notes are an integral part of the consolidated financial 
                                  statements.
<PAGE>
 
                                                                     Form 10-QSB
                                                  United Park City Mines Company
                                                                   June 30, 1998
                                                                          Page 5

                UNITED PARK CITY MINES COMPANY AND SUBSIDIARIES
                      CONSOLIDATED STATEMENT OF CASH FLOWS
                                  (Unaudited)
<TABLE>
<CAPTION>
                                                               For Six Months Ended
                                                             ------------------------
                                                               June 30,     June 30,
                                                                1998         1997
                                                             ----------   -----------
<S>                                                          <C>          <C>
Cash flows from operating activities:
  Net loss.................................................  $ (793,569)  $(1,015,507)
                                                             ----------   -----------
  Adjustments to reconcile net loss to net
    cash used by operating activities:
     Depreciation..........................................     260,087       239,409
     Increase (decrease) from changes in:
      Accounts receivable..................................     (63,561)     (189,996)
      Prepaid expenses and inventory.......................      76,432        87,679
      Hidden Meadows development costs.....................     471,710       442,539
      Deferred development costs-other.....................    (372,596)      (44,147)
      Accounts payable and accrued liabilities.............    (256,841)     (368,762)
      Contracts payable....................................     (65,000)
                                                             ----------   -----------
          Total adjustments................................      50,231       166,722
                                                             ----------   -----------
Net cash used by operating activities......................    (743,338)     (848,785)
                                                             ----------   -----------
                                                           
Cash flows from investing activities:                      
  Construction-in-progress.................................     (20,395)       14,402
  Capital expenditures.....................................     (35,455)      (75,048)
                                                             ----------   -----------
Net cash used by investing activities......................     (55,850)      (60,646)
                                                             ----------   -----------
                                                           
Cash flows from financing activities:                      
  Costs related to issuing stock for land..................     (45,294)
  Proceeds from notes payable..............................                   360,700
  Proceeds from sale of stock under employee option........                    28,632
  Principal payments on bank note payable..................                  (434,704)
                                                             ----------   -----------
Net cash used by financing activities......................     (45,294)      (45,372)
                                                             ----------   -----------

Net decrease in cash and cash equivalents..................    (844,482)     (954,803)
Cash and cash equivalents-beginning of period..............   3,360,878     1,050,405
                                                             ----------   -----------
Cash and cash equivalents-end of period....................  $2,516,396   $    95,602
                                                             ==========   ===========
</TABLE>


  The accompanying notes are an integral part of the consolidated financial 
                                  statements.
<PAGE>
 
                                                                     Form 10-QSB
                                                  United Park City Mines Company
                                                                   June 30, 1998
                                                                          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 1997 Annual Report to Stockholders 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 June 30, 1998 and the consolidated
statements of operations and cash flows for the three month periods and the six
month periods ended June 30, 1998 and June 30, 1997 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 at June 30, 1998 and
for all periods presented have been made.

NOTE 2  IMPACT OF RECENTLY ISSUED ACCOUNTING STANDARDS

The Company has reviewed all recently issued Financial Accounting Standards in
order to determine their effects, if any, on the results of operations or the
financial position of the Company.  Based upon that review, the Company believes
that none of the pronouncements will have a significant effect on current or
future earnings or operations.

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 Empire
Canyon Resort development (formerly known as the Flagstaff Mountain in Deer
Valley project). The Company exchanged 203,700 shares of its capital stock for
the land.
<PAGE>
 
                                                                     Form 10-QSB
                                                  United Park City Mines Company
                                                                   June 30, 1998
                                                                          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") closed the sale of five lots in the Hidden Meadows subdivision during
the first six months of 1998. Blue Ledge recognized a profit of $486,104 on
gross sales of $1,090,000.  The cash proceeds from these lot sales were used to
fund some of the Company's operations.

Since the end of the second quarter of 1998, Blue Ledge has an additional two
lots in the Hidden Meadows subdivision under contract to sell.  The cash
proceeds from these lot sales will also be used to fund some of the Company's
operations.

The Company expects Wasatch County's approval of the master plan for the
Company's twelve lots which adjoin the Deer Crest development project during the
last half of 1998.  The Company has four of the twelve lots under contract to
sell in this project.  These sales are subject to the final recordation of the
master plan and plat which is anticipated during the last half of 1998.

During the second quarter of 1998, the Company resumed discussions with Park
City Municipal Corporation ("Park City") regarding the annexation of its Empire
Canyon project (formerly known as Flagstaff Mountain in Deer Valley).  The
Company is combining its Bonanza Mountain Resort project into the master plan of
the Empire Canyon project and is pursuing the annexation and master plan
approval of the two projects with Park City and Wasatch County as one master
planned project. The Company anticipates master plan approval of the combined
projects during the second half of 1998.

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

The Company's cash balance decreased $844,482 during the first six months of
1998, leaving a cash balance of $2,516,396 as of June 30, 1998.  During the
first quarter of 1998, the Company's operating activities used cash of $743,088
as compared to cash used in 1997 for the same period of $848,785.  The Company
will use a portion of the June 30, 1998 cash balance along with a portion of the
proceeds from future real estate sales by Blue Ledge and revenues from its
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 1998.


RESULTS OF OPERATIONS

1998 Compared with 1997
-----------------------

As previously stated under the Liquidity and Capital Resources - Real Estate
section, Blue Ledge sold five lots in the Hidden Meadows subdivision for a
profit of $486,104 or 45% of the gross sales price during the first six months
of 1998.  Blue Ledge sold five lots in the Hidden Meadows subdivision for a
profit of $345,308 or 40% of the gross sales price of these lots during the same
period in 1997.
<PAGE>
 
                                                                     Form 10-QSB
                                                  United Park City Mines Company
                                                                   June 30, 1998
                                                                          Page 8

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

During the first six months of 1998, the Silver Mine Adventure generated
revenues of $631,733 and incurred $745,221 in operating expenses as compared to
revenues of $633,099 and operating expenses of $891,051 for the same period in
1997. The decrease of $145,830 or 16% in expenses is primarily the result of
revised operating procedures. The Company expects increased numbers of visitors
to the tour in 1998 as a result of increased promotions and an increase in
summer tourism in the Park City area. The Company continues to believe that the
Silver Mine Adventure will cover its direct operating costs in the near future
and will generate sufficient future net cash flows to recover the related
capitalized costs.

The Company's interest income increased 1,110% during the first six months of
1998, when compared with the first six months of 1997.  The increase in interest
income is due to larger cash balances available for investment during 1998.

General and administrative expense decreased 14% during the first half of 1998,
when compared with the same period in 1997.  The decrease is primarily due to
decreased costs associated with research on various projects for possible future
development and operations.

Increased labor and material costs resulted in an increase in mine maintenance
and administrative costs of approximately 33% during the first half of 1998 when
compared with the first half of 1997.  The increase in such costs is due to the
Company's allocation of personnel and resources to its tunnel maintenance
activities.

Charges for depreciation increased 5% during the first six months of 1998 when
compared with the same period in 1997.  This increase is a result of additional
capital assets used in the Silver Mine Adventure being placed in service during
1998.
<PAGE>
 
                                                                     Form 10-QSB
                                                  United Park City Mines Company
                                                                   June 30, 1998
                                                                          Page 9


                                   PART II.
                               OTHER INFORMATION


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

At the annual meeting of stockholders held June 3, 1998, votes were cast as
follows for the election of directors:

----------------------------------------------------------------
                                  FOR            WITHHELD *
----------------------------------------------------------------
Alan L. Gordon                    2,876,073           5,476
----------------------------------------------------------------
Joseph S. Lesser                  2,875,999           5,550
----------------------------------------------------------------
Edwin L. Osika, Jr.               2,874,438           7,111
----------------------------------------------------------------
William H. ("Hank") Rothwell      2,874,221           7,328
----------------------------------------------------------------

* There were no abstentions or broker non-votes as to this election of
directors.

No other matters were submitted to be voted upon by the stockholders.


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
                                                                   June 30, 1998
                                                                         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)


   /s/ Edwin L. Osika, Jr.                         /s/ Michael R. Salmond
--------------------------------                --------------------------------
       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:  August 13, 1998
       ---------------