In this book, there are six chapters, in addition to summary of the research and references indicated in the book. Chapter 1 is Introduction, in which the general introduction on the subject of wave propagation in elastic medium is presented first. The following problems are discussed respectively, at Chapter 2, 3, 4, 5 and 6: (I) The problem of quasi P- wave incident upon a corrugated interface between two dissimilar monoclinic elastic half-spaces. (II) The problem of plane (P/SV ) waves, incident upon a corrugated interface between two dissimilar fibre-reinforced elastic half-spaces. (III) The problem of qP-wave incident at a corrugated interface between two dissimilar pre-stressed elastic half-spaces. (IV) The problem SH-wave incident at a corrugated interface between two dissimilar perfectly conducting selfreinforced elastic half-spaces. (V) The problem of shear wave at a corrugated interface between two dissimilar fibre-reinforced elastic half-spaces. In the end, summary of the research works and list of the references mentioned at various places in the entire book have been given.