Abstract: In this paper, a discrete model of numerical analysis block element method (BKEM) is presented. The basic unknown quantities in this method are the rigid displacements of the block elements. Based on the equilibrium conditions of the loads acting on the blocks and the stresses in the joints between the blocks, deformation compatibility conditions and constitutive law of the joint material, the governing equations can be derived with variational principle. Owing to the different displacements of two adjacent elements, the element is a type of discontinuous displacement element. The convergency for BKEM has been proved with generalized variational principle. By presenting different constitutive law of joint material, elasticity, plasticity and viscosity of structure can be considered. This method can be used to solve discontinuous medium problems, especially to find deformation, stress and stability of rock mass which contains numerous joints and fissures. Research and numerical examples show the method has the advantages of high efficiency and high accuracy.