Two phase masonry model, which contains elastic mortar and elastic bricks, is analyzed numerically in order to evaluate sensitivity of effective elastic moduli and strength properties to a deviation in the masonry structural parameters. Different methods of masonry homogenization are studied. Effective elastic moduli of the masonry representative volume element are obtained by means of direct finite element simulation and homogenization procedure. Influence of variation in the heterogeneous material microstructure characteristics (influence of brick aspect ratio and orientation angle) on the local stress-strain state and mechanical properties of the representative volume element of the composite considered is analyzed. Mechanical properties obtained by direct finite element modeling and other methods in various literary sources are compared. These studies are relevant for the design of composite materials with a structure similar to masonry.