Abstract: The present paper is concerned with the application of boundary element method to plane orthotropic elasticity.In this paper,some basic problems of BENI for plane orthotropic clasticity,such as the gencral fundamental solutions,C-matrix,G_ii-matrix and the expression of stresses at any internal point,are systematically studisd,Based upon this theory,the formulae of constant boundary element and linear boundary element are established.Finally,to illustrate the correctness and the accuracy of the theory and method mentioned above,the stresses in the orthotropic plates with a hole are calculated.It is found that the results are very consistent with the analytical solutions.