Abstract：The upper bound finite element method is one of the commonly used methods for slope stability analysis. Since the Mohr-Coulomb shear yield criterion which is widely used overrates the tension strength，the tensile cracks cannot be get at the rear of the slope when using it for slope stability analysis. In order to solve this problem，the yield surface approximation method of the upper bound finite element method was remolded. From the viewpoint of discrete spatial orientation the plastic flow constraint equation on the discrete directions can be built easily，and by introducing the tension damage to the upper limit method，each azimuth plane was satisfied the tensile failure criteria，and then the linearized upper bound finite element method considering both tension and shear failures can be established. This method can be used to calculate the safety factor of slope and get the critical velocity field with tensile crack. A few of examples prove the effectiveness of this method.