Abstract:In this paper,three-dimensional numerical manifold method (NMM) based on hexahedron element is proposed and the shape functions of C8 isoparametric element are used as the cover weight functions. All sub-matrices of equilibrium equations are derived according to this cover weight function. In 2D contact,the direction of shear stiffness and friction force is easily defined along the contact edge. For the corresponding 3D contact problem,it is difficult to determine similar relations in simple way. In the present paper,vector theory and iterative method are proposed to overcome this kind of difficulty. An example of underground excavation is also presented.