Abstract: The analysis of geophysical and geological data on tectonic processes occurring in the peripheral layers of the Earth, under the influence of local heated mantle material elevations from the lower mantle is conducted. The assumption that there is a difference between the densities of substances originating from the lower mantle and substances of the overlying asthenospheric layer is used. Here, this process is considered as a process of hydrodynamic instability. Physical model of high-viscosity liquids at low Reynolds numbers is used to describe the process. Based on analysis data in the literature on the mantle and salt diapirism, a mechanical-mathematical model of mantle material elevation process through the density difference between the overlying and underlying layers is proposed. An analytical solution of a mathematical problem resulting from application of mechanical-mathematical modeling of mantle diapirism is obtained. Comparison of the results of the analytical solution shows good agreement with the data obtained from the experiments and observations of the salt dome.