The design, construction and operation of high-rise earth dams in seismic regions, such as the territory of the Republic of Uzbekistan, requires constant improvement of the methods to calculate them under various loads, both of a static nature (gravitational forces, hydrostatic, etc.), and of a dynamic nature, including seismic effects. Emergency situations at such facilities or their partial destruction under any impact can lead to disastrous aftermath. The aim of this study is to develop a mathematical statement and an algorithm for numerical solution to an unsteady-state problem for an earth dam in a plane elastic statement. To verify the proposed methodology and the corresponding complex of applied programs, a solution to the test problem was given (the Lamb’s problem). According to the developed methodology and algorithm based on numerical method of finite differences, the problem of studying the stress-strain state was solved under shear stress on the foundation (in the form of a seismogram) on the example of the high-rise Charvak earth dam located near Tashkent city. The solution is presented in the form of distribution lines of equal displacements, stresses along the dam body, depending on time. The most vulnerable zones of the earth dam under consideration were identified.