This work considers analytical calculation of brickwork barrel vault, material structure of which has a pronounced variability of elastic constants. In normative documents, brickwork is considered as a complex two-component building material with elastoplastic properties. However, there are no clear recommendations that consider the variability of the elastic properties of brickwork. This article considers influence of anisotropic properties of a brickwork three-centered flat-arched vault on its stress condition on the basis of the elasticity theory. The calculation of a flat-arched vault is based on the classic theory of bending a curved curvilinearly-anisotropic beam in view of the properties of brickwork materials with cylindrical anisotropy. We cite a mathematical solution of a differential equation of fourth order in partial derivative with two variables for an anisotropic orthotropic body in polar coordinates for creation of mathematical models describing changes in the vault material elasticity modulus. Based on the solution to the curved orthotropic body anisotropy problem, we obtained correlations between elastic constants in the main anisotropy directions.