The study evaluates how dissipation influences wave phenomena through a visco-poroelastic sandy layer and a visco-poroelastic semi-infinite half-space where initial stress exists. The model includes analysis of both poroelastic and viscoelastic characteristics together with detailed studies of solid-fluid phase connections in porous materials. The mathematical model relies on coupled equations that describe the mechanics of porous media, emphasizing the effects of viscosity and porosity on wave speed, attenuation, and dissipation. Influence of several parameters including initial stress, viscosity, porosity, and dissipative effects on wave propagation are demonstrated numerically. Applications in Material Science, seismic exploration, Geotechnical Engineering can benefit from the findings, which offer valuable insights on how waves behave in porous media.