Design, construction, and reliable and safe operation of earth dams (more than 60 of them are in operation in the Republic of Uzbekistan located in seismic region) put forward requirements for the continuous improvement of the calculation methods for loads; as required by regulatory methods for fundamental (static) and special (dynamic) load combinations. These regulatory methods do not take into account the nonhomogeneous nature of the behavior and piecewise heterogeneity of the characteristics of foundation, and the stress-strain state (SSS) of an earth dam under constant or temporary loads, which is necessary for reliable and safe operation, especially in seismic regions. A general mathematical formulation of problems for earth dams in a plane elastic formulation is given. Dynamic calculations were conducted to determine the stress-strain state of an earth dam, taking into account the design features and real piecewise-nonhomogeneous physical and mechanical characteristics of soil of the structure body and base (these characteristics were provided by the design organization). The problem was solved by the numerical finite element method. The eigenfrequencies and modes of vibrations of the plane "structure-foundation" system are determined, considering the homogeneous and piecewise-nonhomogeneous characteristics of the foundation soil; the corresponding analysis of the behavior of the system was made. The stress-strain state of the “dam-foundation” system was investigated using calculated frequencies. The calculation results were lines of equal displacements (horizontal, vertical), normal and shear stresses in the “dam-foundation” system.