In this paper a mathematical model for the extraction-injection of geothermal reservoir in multiple wells is developed, It silplidies a complicated tridimentionsl heat conduction problem to a bi-dimentional one, The latter is a problem of coupling equations, one of wbich is a one-dimentional heat conduction equation in vertical, and another is a one-dimentional convection-conduction eqyation in horizontal, It deduces several different schemes for coupling solutions as the differential equations are discrtized, and discusses the procecdure of computation, We have prepard the software for drwing the groundwater has been exploited with double wells, three wells and five wells.