Wave propagation in poroelastic and viscoelastic solids treated by the Boundary Element method in time domain is the topic of this research book. A novel boundary element formulation has been presented based on the Convolution Quadrature Method. Because in this time-stepping formulation only Laplace domain fundamental solutions are needed this method can be effectively applied to a plenty of problems, e.g., anisotropic or transversely isotropic continua. So, this method combines the advantage of the Laplace domain with the advantage of a time domain calculation. Here, wave propagation phenomenon in viscoelastic as well as poroelastic half spaces are considered. The Rayleigh wave as well as the slow compressional wave in the poroelastic solid is discussed.