Abstract: In this paper,we establish the theory for boundary element method and its application in potential problems.The boundary element method starts from the control equation and boundary value conditions,sets boundary integral equations with weighte residual method,splits the boundary into elements and obtains the linear algebraic equations.In this paper,the boundary element method of constant and linear element for potential problems in 2-dimensional space is discussed.This method reduces the number of space dimension,makes the equation system lower order,less data input and higher efficiency.