The problems of formation and propagation of surface seismic waves in vertically layered and horizontally inhomogeneous media are studied. A mathematical model has been developed for the propagation of surface seismic waves in an inhomogeneous medium based on the use of the fundamental principles of wave dynamics and Fourier transforms. The existence of various types of groups of these waves is proved, and their main properties are studied. It has been established that the reflection coefficients of different groups of a dispersive wave on models of half-spaces (a layered, inhomogeneous medium) with a sharp velocity differentiation are characterized by the same dependence on the angle of incidence as in the absence of dispersion. In the region of the critical angle, which depends on the period of the incident wave, a local decrease in the intensity of wave reflection is observed, which is associated with the origin of the head dispersive wave. It has been found that the reflection coefficients of Rayleigh waves from low-velocity layers, thin (d / λ2 = 0.205) and thick (d / λ2 = 0.82) are approximately 0.2 ± 0.04 and practically do not change with increasing angle of incidence. On the basis of theoretical studies, it was revealed that reflected surface waves carry information both about the elastic properties of the reflecting medium and about the dimensions of the reflecting horizontal inhomogeneity. An experimental dispersion curve of the group velocity of Rayleigh waves on the Central Asia-Caucasus path has been obtained. The seismic stress state of the "subgrade-base" system was studied. Based on the analysis of the results of numerical experiments, it has been established that in order to obtain a complete picture of the seismically stressed state of the subgrade, it is necessary to take into account the contribution to it of each component of the accelerogram of a real earthquake.