Abstract: Various types of hardening laws have been in the formulation of the elasto-plastic constitution relationship of soil. In this paper, the influence of different hardening laws on the matrix of elasto-plastic modulus Dep of soil is studied, and the appraoch for establishing the yield locus and plastic potential is proposed. The general expressions of Dep which can be used is the finite element analysis for the three-Dimensional, plane strain and axisymmetrical case are devide.