Abstract: Compared with the limit equilibrium method, the lower limit analysis has a more rigorous mechanics foundation, and the safety factor acquired by the lower limit analysis is more conservative and valuable. Although many scholars have done many useful researches on it, however, the classical linearization method cannot solve the general problem of the anisotropy of strength. In this paper, spatial discretization is implemented, and the yield criterions on the discrete directions are built. Finally, pseudo cohesion is introduced to keep the property of lower bound analysis. The examples show that the result can converge to exact solution stably from below. Proposed method not only enriches the lower bound theory based FEM and linear programming, also lays a solid foundation for anisotropic problems.