Comprehensive analysis of the possible approaches to determining the strength of masonry was performed. The classical theories of strength is not suitable for this purpose due to absence of taking into account the anisotropy of masonry, which determines the presence of a complex relation between the strength and the orientation of principal stresses to mortar joints. Russian and foreign criteria of masonry strength were evaluated. It is shown that these criteria are only suitable for in-plane stress and require a large amount of input data, which are extremely difficult to obtain. Fundamental approaches to the finite element modeling of masonry were considered. On the basis of these approaches the simulation of few brick vaults was performed. According to the results of simulation and analysis of existing criteria, it was proposed to adapt these criteria for the case of triaxial stress state and also develop the strength tests of masonry samples simulation model as source for input data.