The embedded softening surface is used to simulate the propagation of fracture in rocks. Based upon the virtual work principle

the equilibrium equations of FEM considering the effect of fracture on deformation are established. And on the basis of the complement virtual work principle

the concrete matrix for the effect of fracture is deduced. As an example

the first type of fracture-cracking problem is analyzed to develop the visco-plastic constitutive relationship on crack surfaces

the visco-plastic FEM calculation procedure is then obtained. Finally

an example is simply calculated to demonstrate the rationality of the proposed method.