<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 SEPTEMBER 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)


                                (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:  As of November 13, 1998: 3,249,411
                                            ----------------------------------
shares
------

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

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

<TABLE>
<CAPTION>
                                                                   September 30,
                                                                        1998
                                                                   -------------
<S>                                                                <C>
ASSETS:
Cash and cash equivalents.........................................   $2,027,483
Accounts receivable...............................................       19,747
Prepaid expenses..................................................       43,957
Material and supplies inventory...................................      232,556
Deferred income taxes.............................................      475,202
Other.............................................................       11,100
                                                                   ------------
                                                                      2,810,045
                                                                   ------------

Real Estate:                                                                   
  Subdivision development.........................................    1,043,524
  Deferred development costs......................................    1,886,328
                                                                   ------------
                                                                      2,929,852
                                                                   ------------
Property and Equipment:                                                        
  Mine shaft, buildings, and equipment............................    4,103,940
  Mine tour attraction............................................    4,899,061
  Construction-in-progress........................................      273,008
  Resort facilities...............................................       58,077
  Less accumulated depreciation...................................   (4,804,765)
                                                                   ------------
                                                                      4,529,321

Land less accumulated depletion of $1,062,190.....................   12,795,003
Water rights......................................................      400,000
                                                                   ------------
                                                                     17,724,324 
                                                                   ------------


Total assets......................................................  $23,464,221
                                                                   ============

</TABLE>

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

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

<TABLE>
<CAPTION>
                                                                 September 30,
                                                                      1998     
                                                                 -------------
<S>                                                              <C>    
LIABILITIES AND STOCKHOLDERS' EQUITY:                                           
Accounts payable..............................................     $   432,839
Accrued liabilities...........................................         611,243
                                                                 -------------
  Total liabilities...........................................       1,044,082
                                                                 -------------
                                                                 
                                                                 
                                                                 
                                                                 
                                                                 
                                                                 
                                                                 
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..............................      41,982,640
  Accumulated deficit.........................................     (19,411,211)
                                                                 -------------
                                                                    22,603,923  
                                                                 
  Less cost of treasury stock - 1,294 shares..................        (183,784)
                                                                 -------------
                                                                 
  Total stockholders' equity..................................      22,420,139
                                                                 -------------
                                                                 
Total liabilities and stockholders' equity....................     $23,464,221
                                                                 =============
</TABLE>

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

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

<TABLE>
<CAPTION>
                                                For Three Months Ended          For Nine Months Ended
                                             ----------------------------    ---------------------------- 
                                                Sept. 30,     Sept. 30,         Sept. 30,     Sept. 30,
                                                  1998          1997              1998          1997
                                             -------------  -------------    --------------  ------------
<S>                                          <C>            <C>              <C>             <C>
Revenues:
 Lot sales................................    $  359,000                       $ 1,449,000   $   855,000        
 Mine tour attraction.....................       526,542      $  520,906         1,158,315     1,154,005                  
 Interest.................................        30,217           5,495           101,871        11,427                  
 Royalties and rentals....................           250         (35,501)          142,255       146,009                  
 Contract services........................         1,389             234            64,054        60,787                  
 Other....................................        27,552          16,899            33,637        58,395                  
                                              ----------      ----------       -----------   -----------  
                                                 944,950         508,033         2,949,132     2,285,623                  
                                              ----------      ----------       -----------   -----------
 
Expenses:
 Cost of lot sales and selling expense....       215,593          69,459           819,489       579,151                 
 Mine tour attraction.....................       457,926         454,628         1,203,147     1,345,679                 
 General and administrative costs.........       161,152          39,737           675,657       637,416                 
 Mine maintenance and administrative                                                                                
   costs..................................       762,278         369,375         1,373,432       828,392                 
 Contract services costs..................           851             181            38,133        42,935                 
 Depreciation.............................       128,703         114,345           388,789       361,816                 
 Interest.................................         7,145          33,677            32,752        79,110                 
                                              ----------      ----------       -----------   -----------   
                                               1,733,648       1,081,402         4,531,399     3,874,499                  
                                              ----------      ----------       -----------   -----------    

Loss before income taxes..................    $ (788,698)     $ (573,369)      $(1,582,267)  $(1,588,876)                  
                                                                                                                           
 Income tax benefit.......................             0               0                 0             0                   
                                              ----------      ----------       -----------   -----------                   

Net loss..................................    $ (788,698)     $ (573,369)      $(1,582,267)  $(1,588,876)                  
                                              ==========      ==========       ===========   ===========                   

Basic and diluted net loss per share......    $    (0.24)     $    (0.19)      $     (0.49)  $     (0.56)                  
                                              ==========      ==========       ===========   ===========                   

Basic and diluted weighted average number 
of shares outstanding.....................     3,249,411       2,955,314         3,212,103     2,812,800                   
                                              ==========      ==========       ===========   ===========    
</TABLE>

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

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


<TABLE>
<CAPTION>
                                                                                  For Nine Months Ended
                                                                           ------------------------------------
                                                                               Sept. 30,          Sept. 30,
                                                                                 1998               1997
                                                                           ----------------   -----------------
<S>                                                                        <C>                <C>
Cash flows from operating activities:
  Net loss..........................................................         $(1,582,267)         $(1,588,876)       
                                                                             -----------          ----------- 
  Adjustments to reconcile net loss to net                                                                           
  cash used by operating activities:                                                                                 
     Depreciation...................................................             388,789              361,816        
     Increase (decrease) from changes in:                                                                            
      Accounts receivable...........................................              76,273             (533,773)       
      Prepaid expenses and inventory................................             109,050              (53,190)       
      Subdivision development costs.................................             637,426              443,325        
      Deferred development costs....................................            (678,397)            (152,826)       
      Accounts payable and accrued liabilities......................             (20,283)            (275,284)       
      Contracts payable.............................................             (65,000)                            
      Other.........................................................                   -             (124,705)       
                                                                             -----------          ----------- 
          Total adjustments.........................................             447,858             (334,637)       
                                                                             -----------          ----------- 
Net cash used by operating activities...............................          (1,138,952)          (1,923,513)       
                                                                             -----------          -----------

Cash flows from investing activities:                                                                                
  Construction-in-progress..........................................             (52,816)               8,007        
  Capital expenditures..............................................             (99,120)             (54,002)       
                                                                             -----------          ----------- 
Net cash used by investing activities...............................            (151,936)             (45,995)       
                                                                             -----------          -----------   
Cash flows from financing activities:                                                                                
  Costs related to issuing stock for land...........................             (47,050)                            
  Proceeds from rights offering.....................................                                5,440,000        
  Proceeds from sale of stock under employee option.................                                   28,644        
  Principal payments on bank notes payable..........................                                 (431,116)       
                                                                             -----------          ----------- 
Net cash provided (used) by financing activities....................             (47,050)           5,037,528        
                                                                             -----------          -----------   

Net increase (decrease) in cash and cash equivalents................          (1,333,395)           3,068,020        
Cash and cash equivalents-beginning of period.......................           3,360,878            1,050,405        
                                                                             -----------          ----------- 
Cash and cash equivalents-end of period.............................         $ 2,027,483          $ 4,118,425         
                                                                             ===========          =========== 
</TABLE>

       The accompanying notes are an integral part of the consolidated 
                             financial statements.
<PAGE>
 
                                                                     Form 10-QSB
                                                  United Park City Mines Company
                                                              September 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") and the Form 10-QSB for the periods ended March 31, 1998 and June 
30, 1998.

B.   Management's Representation

The consolidated balance sheet as of September 30, 1998 and the consolidated
statements of operations and cash flows for the three month periods and nine
month periods ended September 30, 1998 and September 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 September 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 Flagstaff
Mountain Resort development.  The Company exchanged 203,700 shares of its
capital stock for the land.
<PAGE>
 
                                                                     Form 10-QSB
                                                  United Park City Mines Company
                                                              September 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") sold seven of the lots in the Hidden Meadows subdivision during the
first nine months of 1998.  Blue Ledge recognized a profit of $629,511 on the
gross sales of $1,449,000 during this nine month period.  The cash proceeds from
these lot sales were used to fund some of the Company's operations.  Five of
these lots sales occurred during the first six months of the year and two lot
sales were completed during the third quarter of 1998.

During the third quarter of 1998, the Company received from Park City Municipal
Corporation ("Park City") approval of the parameters by which Park City would
annex and approve the master plan for the Company's Flagstaff Mountain project.
The Company has combined its Bonanza Mountain Resort project into the master
plan of the Flagstaff Mountain 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 first half of 1999.

The Company has received approval from Wasatch County for eight lots of its
twelve lot master-planned project which adjoins the Deer Crest development
project.  The Company is proceeding with this development and has four of the
approved lots in this project under contract for sale.  These four sales are
expected to be finalized during the fourth quarter of 1998.

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

The Company's cash balance decreased $1,333,395 during the first nine months of
1998, leaving a cash balance of $2,027,483 as of September 30, 1998.  The
Company will use a portion of the September 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 and 1999.

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

The year 2000 issue concerns the potential impact of computer software and
embedded computer processor chips being unable to accurately process data during
and after the year 2000.  As a result, all business and government entities are
at risk for possible miscalculations or systems failure causing disruptions in
operations.  This problem is commonly known as the Year 2000 Issue ("Y2K").  As
the Company uses computers and software in its financial, sales, maintenance,
development and engineering operations,  this issue or problem could arise at
any point in its normal operations.

The Registrant and its operating subsidiaries have implemented a plan to review
and update its information systems (computers and software) to insure that its
systems are Y2K compliant and minimize, as much as possible, any impact from Y2K
problems that the Company or the Company's suppliers may encounter.  The first
component of the Company's plan is to review, with its own staff and outside
consultants, its information systems.  This component of the plan is nearing
completion.  While not yet complete, the Company has discovered, like most other
companies, that several of its software
<PAGE>
 
                                                                     Form 10-QSB
                                                  United Park City Mines Company
                                                              September 30, 1998
                                                                          Page 8

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

programs and computers are not Y2K compliant. While the problem is not
extensive, the Company is at risk to a minor degree.

The second component of the Company's plan is to remedy, correct or update its
information systems to make the systems Y2K compliant. While the first component
of the Company's plan is not yet complete, the Company's staff have been
reviewing the currently identified problems with its software suppliers and
consultants in an effort to identify the extent of the problem and the costs to
actually remedy the presently identified problems. At the current time, those
costs do not appear to be either material or significant and are in the
thousands of dollars, rather than the tens of thousands of dollars range.

The third component of the Registrant's plan is to identify and contact through
letters and interviews significant service providers, vendors, suppliers and
government entities that the Company believes to be critical to its normal
business operations after January 1, 2000, in an effort to ascertain both their
preparedness for the Y2K problem and the impact which their unpreparedness for
the Y2K problem could have upon the Company. In most cases, those service
providers, vendors, suppliers and government entities have exhibited a high
degree of awareness of the problem and have willingly provided information
concerning their state of readiness for the Y2K problem. This third component of
the plan is still ongoing.

As part of the Registrant's plan, the Company is developing contingency measures
intended to mitigate the possible disruption of its normal business operations
that may result from the Y2K issue and to identify the costs for such plans.
Contingency measures may include stockpiling materials, securing alternative
sources of supplies, adjusting hours of operations and work-force, manual
operation of facilities and the manual recording and manipulation of data.
Because of the Company's small size, the costs of contingency measures are not
expected to be either material or significant.



RESULTS OF OPERATIONS

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

As previously stated under the Liquidity and Capital Resources - Real Estate
section, Blue Ledge sold seven lots in the Hidden Meadows subdivision, for a
profit of $629,511 or 43% of the gross sales price of these lots, during the
nine months period ended September 30, 1998.  During the same period in 1997,
Blue Ledge sold five lots in the Hidden Meadows subdivision for a profit of
$275,849 or 32% of the gross sales price of these lots.

During the first nine months of 1998, the Silver Mine Adventure generated
revenues of $1,158,315 and incurred $1,203,147 in expenses as compared to
revenues of $1,154,005 and expenses of $1,345,679 for the same period in 1997.
The Company expects increased numbers of visitors to the tour as a result of
additional promotions and increases in group tour bookings during the fourth
quarter of 1998.  The Company continues to believe that Silver Mine Adventure
will contribute to the Company's cash flows in the future.

The Company's interest income increased 791% during the first nine months of
1998, when compared with the first nine months of 1997.  The increase in
interest income is due to larger cash balances available for investment during
1998.
<PAGE>
 
                                                                     Form 10-QSB
                                                  United Park City Mines Company
                                                              September 30, 1998
                                                                          Page 9

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

Other revenues decreased 42% during the nine month period ended September 30,
1998 when compared to the same period in 1997. The decrease is primarily the
result of fewer scrap metal sales being made in 1998 as compared to 1997.

Increased consultant, material and legal costs resulted in an increase in
general and administrative costs of approximately 6% during the first nine
months of 1998 when compared with the first nine months of 1997. The increase is
primarily due to increased costs associated with research on various projects
for possible future development or operations.

Increased labor, material and contractor costs resulted in an increase in mine
maintenance and administrative costs of approximately 65% during the nine months
period ended September 30, 1998 when compared with the same period in 1997. 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 and
mitigate problems with water drainage from its vast mountainous properties.

The Company's interest expense deceased 59% during the first nine months of
1998, when compared to the same period in 1997. This decrease in interest
expense is the result decreased bank borrowings and borrowings from third
parties during the nine months ended September 30, 1998.
<PAGE>
 
                                                                     Form 10-QSB
                                                  United Park City Mines Company
                                                              September 30, 1998
                                                                         Page 10


                                   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 third 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
                                                              September 30, 1998
                                                                         Page 11


                                  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/ Micahael 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: November 13, 1998
      -----------------