Abstract <p>Weather conditions in the Far North require the use of pile foundations for multi-story buildings. Unlike mid- and equatorial latitudes, it is impossible to strengthen the soil between the piles; on the contrary, the properties and geometry of the subsidence of this soil depend on weather conditions. In this paper, the grid-characteristic method on systems of individual pairwise non-conformal curvilinear and Cartesian grids is used to solve inverse problems of determining the strength properties of piles and foundations of buildings operated in the Far North. To solve the inverse problem, a software package has been developed that uses an iterative solution of direct problems. The method allows one to vary such values as pile length, wavelength, number of piles per room, pile thickness, soil subsidence and its shape, elastic properties of the surrounding geological environment, number of floors, ceiling height, wall thickness, etc. In order to demonstrate the capabilities of the proposed method, a number of dependencies of strength characteristics on variable parameters were obtained.</p>