Abstract:An element splitting technique is introduced into the finite element method which simulates the failure of rock material including tension and shear;the failure criterion of this method is based on Mohr-Coulomb criterion and Griffith criterion. This method adopts contact elements to describe the breakage interfaces in material. The application of dynamic relaxation method will complete this solution without generating the global stiffness matrix,which is difficult for traditional FEM when the topology of model is changing. The validation of this method is verified by two examples of three-point bending and uniaxial compression