The three-dimensional numerical manifold with high-order displacement functions has been developed based on the tetrahedron element meshes. The global equilibrium equations of high-order manifold method are established by minimizing the total potential energy. The stiffness matrix

the loading matrix and displacement resistance matrix are derived and added to the global equations. The example of the cantilever bending under the area loading is calculated by the high-order manifold method and the numerical results agree well with theoretical solutions.