Abstract: Based on damage mechanics and theory of masonry structure, a mesoscopic mechanics model of masonry structure is established. In the model, masonry is considered as a composite material consisting of block, mortar and block-mortar interface. The Material Failure Process Analysis (MFPA^2D) system is used to simulate the fracture process of masonry. Under horizontal shear-compression loading condition, the crack propagation process is simulated with this model. The numerical results are in good agreement with experimental observations. It is found that the shear fracture of masonry is predominantly caused by tensile damage.