Abstract:The weight functions and the displacement functions of tetrahedron finite element covers are defined. The global equilibrium equations of three-dimensional numerical manifold method (3D NMM) based on finite element covers are established by minimizing the total potential energy. The stiffness matrix,initial stress matrix,loading matrix,inertia matrix,displacement resistance matrix,contact matrix and friction force matrix are derived and added to the global equations. The numerical results from several typical test cases indicate the proposed method is valid.