The multilayer relaxation of Cu(100),(110),(111)and(311) surfaces are calculated- using the modified embedded atom method,from which the results obtained are in good agreement with the experiments. The self-diffusion mechanisms on the Cu(100) surface are investigated,and the result is colse to the available experimental data and that obtained by local density approximation method.In addition,the diffusion barrier heights on Cu(110) and (111) surface are predicted.