The paper demonstrates a general approach that allows one to solve coupled problems of the interaction of an elastic medium in which non-stationary waves of various types are excited and a vibration-absorbing barrier. For this, the motion of an elastic medium and plates of various types are considered separately. All problems are solved in dimensionless form. To construct solutions, all functions were expanded into trigonometric Fourier series, and the direct Laplace transform in time was applied to them. The problem of determining the kinematic and dynamic parameters of a medium in which waves of various types were induced was solved, the damped plane wave and the cylindrical wave. The solution for the auxiliary problem of determining the surface transient functions for an elastic half-space when a displacement field appears on the boundary of this half-space is obtained. The initial-boundary value problems for transient interaction of elastic media and obstacles are solved. In this case, various approaches were used: for a homogeneous Kirchhoff-Love plate, the results announced in paragraph 3 are used, and for the plate model of Paimushin V.N. the conditions of contact between the medium and the barrier are introduced. Thus, in the image space and in the coefficients of the series, displacements in the soil after the wave passed through the barrier, as well as the stresses and strains, were found. When performing the inverse Laplace transform, it turned out to be impossible to perform the inversion in an analytical way, then the numerical-analytical modified method of F. Durbin was applied. As a result, specific examples of the interaction of barriers and waves in an elastic medium were considered, for which a homogeneous plate equivalent to a three-layer barrier was found. Based on the reduction coefficients found, a conclusion was made about the more effective absorbing properties of a three-layer plate.