Abstract：The purpose of this paper is to study the mesh size sensitivity in rock progressive failure process by taking heterogeneity into consideration. The size of crack tip in the plastic zone is obtained by using classical elasto-plastic theory. Then two numerical models containing a pre-existing crack are conducted to uniaxial compressive loading to investigate the homogeneity effects. Two numerical specimens are divided into the same grid meshes and they have same geometry and size but different heterogeneity. In the other way，four numerical models with the same geometry and size are divided into different meshes to study the mesh sensitivity. Numerical analysis results show that the peak strength of the rock specimens increases as homogeneity increases and crack propagates smoothly until brittle fracture takes place. It also approves that the mesh size should be small enough to fit the need of failure process analysis if the heterogeneities are taken into account in rocks. Mesh size has great dependence on the structural property in homogeneous materials，while mesh size depends on the degree of heterogeneity of the material as well as structural property in heterogeneous materials. Mesh geometry and mesh size adjustment during crack propagation process should be based on the assumption that materials are homogenous.
