A mesoscopic mechanics model for masonry structures is established based on elastic damagemechanics and the tests of masonry structures under shear-compression loading.In the model, it is assumed that the masonry structure consists of matrix,aggregates and interfaces between them. The inhomogeneity of themasonry structure is characterized. The constitutive equation based on elasticdamage mechanics is put forward, using the max tensile-strain criterion andMohr-Coulomb criterion as the damage threshold. At the same time, a stress analysisis carried out, using the Material Failure Process Analysis (MFPA^\rm 2D). Theresults show that the numerical model and the stimulation method can wellstimulate the failure process of the mansonry structure under shear-compressionloading.