A series of numerical experiments are conducted by the Elasto-Plastic CA model, which was successfully used to simulate the rock failure process under uniaxial compression in previous work by the authors, to obtain the failure processes of heterogeneous rocks as well as the stress-strain relation and strain-AE relation under tensile loading at meso level. The model can consider the heterogeneity of the materials conveniently, and has the advantages of localization, parallelization etc. By constructing some local simple rules, the model can perfectly simulate the self-organization process of rock failure process. In this paper, the domain is discretized into the system composed of cell elements which are assumed to conform to the constitutive laws of elasto-brittle-plasticity. The Weibull’s stochastic distribution is introduced to represent the heterogeneity of rock materials, and Mohr-Columb criterion with tension cut-off is considered as the yield criterion. The process of crack initiation, propagation and coalescence is well simulated and the results obtained reproduce the main features known of rock behavior, both at meso and overall stress-strain levels.