The microstructure of masonry, i.e. the complex arrangement of horizontal and vertical joints, their thickness and the mechanical properties of the material of the units and mortar, influences the failure mechanism and strength anisotropy of the compound material. Simplified approaches have been formulated in the past to analyse masonry structural behaviour under vertical and horizontal loading conditions. Owing to the enormous advances of the computational mechanics, a wide spread of numerical modelling techniques have been developed aiming at the simulation of an accurate structural behaviour of masonry. Three-leaf masonry under compression is the most usual construction form in big masonry structures like fortification walls, and walls or piers of monumental buildings of large dimensions. Brick masonry walls are frequently subjected to shear in addition to compression, particularly in seismic regions. For new masonry buildings, the analysis and design for the time being is based on the assumption of a homogeneous material.