The Lagrangian multiplier mesh is applied to simulate the contact property of the bedding plane of rock slope. The weak formulation of the Lagrangian control equations considering the contact constraint conditions and the finite element discrete equations have been derived. The suggestion method can solve the nonlinear and non-smooth problems of the mechanical response perfectly and tolerance large tangential slipping of the contact surface. A bedding rock slope of the Hu-Rong-Xi Expressway is analyzed applying the method mentioned above. The distribution rules of the displacement

stress

strain

contact state

contact friction faoce and sliding distance under the status of critical sliding are obtained. The numerical simulation results indicate that the destruction of the bedding slope is a progressive course. The interlayer stagger firstly

then the deformation evolves to creep bedding slip and the bottom rock occurs burst slide at last. The destruction model changes form the bedding slide to rock burst slide.