A preliminary assessment of the strength of earth dams under dynamic loads is one of the most important tasks associated with the design of such massive hydraulic structures. The present study is devoted to predicting the deformation of earth dams under the influence of strong earthquakes, which are possible in the immediate vicinity of the dam location. Recently, a number of large earthquakes have occurred in the world, which led to severe destruction and indicate high seismic risks associated with the potential instability of existing large earth dams. Under intense seismic impacts, the response of the dam depends on various factors, including its geometric dimensions, as well as the type of structure. A number of existing dams, which were designed and built according to the normative rules of their time, do not take into account modern real operating conditions, in particular, potential seismic loads. This article examines the influence of these factors on the stability and strength of earth dams, taking into account the real properties of the soils of the dam body and the base of the bottom of the hydraulic structure in accordance with the new regulatory requirements. On the basis of the proposed mathematical model, verification calculations for the strength and stability of such earth dams located in the seismic zone were carried out. To assess seismic safety of high earth dams built and operating in regions of complex climatic conditions, including frequent earthquakes, the proof of the method choice capable of reliable and valid results in terms of adopted assessment criteria is required. Correct mathematical model choice ensures, on the basis of computations, strength indices of the hydraulic structure under study. In particular, comparison and analysis of calculated date obtained in case of the plane calculation model and spatial model with the field measurements results and spectral analyses of the Sarsang dam accelerograms showed the suggested calculation models provided reliable strength indices results for the earth dams in the operating reservoirs. The use of more complex models of the physical and mechanical properties of the dams’ soil leads to reliable results that are in good agreement with real field tests.