Abstract: The tangential stress at the boundary can not been gained directly in the application of BEM to analysing elastic stress. In this paper, difference method is used for solving tangential stress at the boundary on the basis of BEM. The difference equations for the boundary tangential stress are derived in the case of constant boundary element. The calculation show that the method in this article is feasible, and simple and practical. The method and equations developed also can been used to calculate the boundary tangential stress in the case of higher boundary element.