The purpose of this paper is mathematical modeling of vertical displacements of the earth surface of the Kaluga underground gas storage. The method proposed by the authors can be used for all underground storage facilities of this type. At the moment, the technology of gas storage in reservoirs is unique and is used only in Russia and China. The development of modern methods for modeling vertical displacements of the earth surface is the most promising direction due to the transfer of gas storage technology throughout the world. Modeling will be carried out at the Kaluga UGS facility. The calculation of the real vertical offsets of the earth surface, taking into account the weight of the overlying rocks, is carried out according to the data on the values of reservoir pressure. Spatial (3D) modeling is carried out in order to determine the configuration of the subsidence surface and its dimensions in conditions when the simulated reservoir is an irregularly shaped figure. For mathematical modeling of the stress-strain state of such objects, a numerical-analytical approach is used. This approach will make it possible to assess effectively the deformation processes caused exclusively by the mode of operation of the UGS facility. © Published under licence by IOP Publishing Ltd.