The boundary element method(BEM)is a new numerical method. As it can reduce the dimensionality of the studied potential field problem, this me thod, as compared with FEM and FDM methods, has such advantages as sim plicity and convenience, less data quantity, rapid calculation and high preci sion. In consequence, this method has been successfully used to solve the cal culation for apparent resistivity anomaly or a three-dimensional geoelectric model which can hardly be worked out by FEM and FDM methods.This paper deals with the principle and numerical processing technique of using BEM method to solve the potential fiel dproblem of the three-dimen-sional geoelectric body of a point source field under the condition of horizon tal or undulate suiface with some calculation examples given: numerical solu tion and analytic solution of apparent resistivity over the conductive spheri cal orebody; plane- section curves or apparent resistivity along different survey lines over a conductive spherical orebody; combined profile curve of apparent resistivity over a conductive ellipsoidal orebody and its topographic correction.The consistency between the numerical solution and the analytic solution of BEM method for apparent resistivity and the obvious effects of three-di mensional topographic correction demonstrate that BEM is an effective method for solving potential field problem of an arbitrary three-dimensional geoelectric model. As it has realized the calculation for spatial potential field over an arbitrary three-dimensional geologic body, this method will undoubtely push forward the electrical prospecting research and play an important role in raising geological effects of the electrical prospecting.