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The paper provides a detailed analysis of the current state of the problem. A mathematical model is presented to determine the dynamic behavior of earth dams, considering the viscoelastic properties of soil, using the hereditary Boltzmann-Volterra theory with the A.R. Rzhanitsyn kernel under periodic kinematic impacts. To solve the problems considered, the finite element method and complex arithmetics were used to reduce integrodifferential equations to a high-order complex algebraic equation. The accuracy of the methods was verified by solving test problems. Steadystate forced vibrations of the Pskem earth dam 195 m high are studied considering the real geometry and soil properties under resonant vibration modes. It was stated that the largest stress amplitudes in the body of the dam occur not only under the first resonance, but they can occur under other dense spectra of the eigenfrequencies of the dam, due to the interaction between close natural modes of vibration. The strength of various sections of the dam body was tested under kinematic impact using the Coulomb- Mohr theory of strength; the most dangerous sections of the dam were identified in terms of the highest stress.