New mathematical models including an oscillation generator and semi-bounded non-uniform in depth foundation possessing porosity, fluid saturation, and viscoelasticity, are considered. The foundation is represented by a poroelastic layer saturated with gas-liquid mixture, a heterogeneous layer with a viscoelastic coating, and a heterogeneous layer with a subsurface liquid sheet. The foundation of the pack of layers is hard. The operation of the surface oscillator is represented as Fourier series, and the problem of steady-state oscillatory conditions is solved. Applying the Fourier integral transform to the equations that describe continuous media under satisfying boundary conditions allows the construction of integral formulas describing the stress-strain condition in the layer package. A numerical algorithm to study the dependence of the ground-wave propagation on the mechanical and geometrical characteristics of the problem is proposed. The models described are widely used in Geophysics, seismic exploration, construction, railway design, and new material designing.