This short paper will present a two-dimensional (2D) model of masonry material. This mesoscopic mechanical model is suitable to simulate the behavior of masonry. Considering the heterogeneity of masonry material, based on the damage mechanics and elastic-brittle theory, the new developed Material Failure Process Analysis (MFPA2D) system was brought out to simulate the cracking process of masonry, which was considered as a three-phase composite of the block phase, the mortar phase and the block-mortar interfaces. The crack propagation processes simulated with this model shows good agreement with those of experimental observations. It has been found that the shear fracture of masonry observed at the macroscopic level is predominantly caused by tensile damage at the mesoscopic level. Some brittle materials are so weak in tension relative to shear that tensile rather than shear fractures are generated in pure shear loading.