In recent years,some progresses are achieved in the research of rock mesoscopic failure,but elastic damage model cannot be adopted simply in many practical projects. Therefore,most important influences of mesoscopic local plastic deformation of rock on strength and stability of rock mass should be considered. An elastoplastic damage mesoscopic model is deduced based on the theory of strain space. The failure elements deleting method is put forward to simulate the crack propagation. If the degree of damage elements equals 1,the code deletes these elements automatically in order to explicitly show how cracks propagate in rock. High-performance parallel calculation is adopted to realize 3D numerical simulation of rock fracture process. The failure processes of marble three-point bending specimens with modes I and I–II cracks are numerically simulated. By setting crystal in crack-tip,transgranular fracture and intergranular fracture are studied. The initiation and propagation of cracks and the failure shapes of the specimens are given. The influence of mesoscopic heterogeneity on rock macroscopic failure mechanical behaviors is analyzed. The calculation results show that the rock mass stability considering mesoscopic local plastic deformation is better than that without consideration of local plasticity. The results of simulation and physical tests accord each other well,which illuminates the validity of the elastoplastic damage failure model. Failure pattern of transgranular fracture and intergranular fracture depends on the intension of crystal. The failure elements deleting method solves the difficult problem of FEM to simulate propagation. The model and method may be valid in practical projects.