The paper reviews in detail the modern state of the calculation problem for non-linear rheological properties of soil in making an assessment of the stress-strain state of ground structures. The mathematical statement, methods and algorithms to assess the dynamic behavior of earth structures taking into account heterogeneous specific features of a structure, linear, non-linear-elastic, non-linear-viscoelastic properties of soil under different dynamic effects are given. The result of a dynamic calculation is the study of unsteady forced oscillations of a number of earth dams taking into consideration non-linear viscoelastic properties of soil and heterogeneous specific features of a structure. The obtained results permit us to reveal several mechanical effects of theoretical and practical value. It was revealed that under high-frequency intensive effect the character of structures oscillations having low-frequency specter has three pronounced stages: an initial one that is characterized with low amplitudes, transitional one, when the swinging of structure occurs; and the stage of free oscillation with realized amplitude and frequency of own vibrations. In spite of the high intensity of high-frequency effect, which causes large stresses in the body of the discussed dams, the calculation of non-linear strain in the material does not greatly distort the pattern of linearly elastic design.