Abstract: The fundamental solution to the governing equation is used as the wei-ghted equation in the boundary element method,by which the region integr-ation can be avoided.But the difficulty will arise when the problem conc-erned is so complicated that it is impossible to find the fundamental solut-ion.In such casesn,non-fundamental functions are occasionally used as we-ighted functions.In this paper the systematic study is made of the relati-ons between the weighted function and boundary integration equation.Two fundamental solutions(Kselvin solution and Laplace solution)are used for various kinds of problems to obtain the integration equation, and a new method for solving the equation is developed by combining the boundary foint equation with the inner point equation.With this method,the diff-culty in finding the fundamental solution is avoided and the convinience is provided for compiling the multi-function conputer program to solve various kinds of problems.