In this book, there are five chapters, in addition to references indicated at the end of the book. Chapter 1 is General Introduction, in which the subject of wave propagation in elastic medium is presented first. Then, some derivations of the Mathematical equations are also explained. Rayleigh"s method of approximation for solving the problems of elastic wave propagation at a corrugated interface has been explained. In Chapter 2, a problem of reflection and transmission of SV-wave at a plane interface between homogeneous and inhomogeneous elastic half-spaces has been investigated. In Chapter 3, a problem of Love wave propagation in a homogeneous isotropic corrugated layer over another isotropic half-space has been analyzed. The dispersion relation for the Love wave propagation has been derived. In Chapter 4, a problem of the propagation of P-wave through a corrugated interface between an ideal liquid and an elastic isotropic half-spaces has been studied. In Chapter 5, a problem of the propagation of SH- wave at a corrugated interface between an elastic solid and a linear viscoelastic liquid half-spaces has been studied.