A two~dimensional mathematical model of a fault controlled geothermal reservoir has been developed. Heated lighter water, rising in the fault, is assumed to charge a reservoir which, in turn, is overlain by a thin impermeable, thermally conducting cap rock. The mass flow rate or the pressure associated with the charging process at the fault inlet is unknown and can only be estimated. Thus, in this paper, the pressure in the fault at the bottom of the reservoir is assumed to be prescribed.