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In the article solves particular problems of the impact of non-stationary external loads on plane structural elements interacting with a deformable medium.The oscillation frequencies and their influence on the dynamic behavior of a plane element under normal load are investigated, as well as the effect of a moving load on the values of transverse displacement. When solving applied problems of oscillations of rectangular plane elements interacting with the environment, a wide class of boundary value problems of oscillations associated with various boundary conditions at the edges of a plane element arises. When taking into account non-stationary external influences, the main of the main parameters is the frequency of natural oscillations of the plane element, taking into account the deformable base, temperature, pre-tension, anisotropy and other factors.