A collection of works is presented in which the author explores mostly via computational modeling the solution of the PDEs governing wave motion in viscoelastic solids and in multi-phase porous materials. The aim: quantifying the dissipative effects on amplitudes, particle polarization, Q attenuation, dispersion, velocities, etc. Maxwell models are considered in the first section of the book. In the second the averaged motions of the solid frame and viscous fluids of porous materials are quantified using Biot, de la Cruz and Spanos and Sahay theories. A variety of finite difference and...