This book presents the main results of extensive research on diffraction, radiation and propagation of elastic waves. In recent years, there has been an increase in interest in problems in the fields of diffraction, radiation and propagation of elastic waves associated with the interaction of bodies both with each other and with media interfaces. In addition, there is currently extensive focus on the solution of three-dimensional wave problems, with the help of Debye potentials, for elastic isotropic and anisotropic bodies of analytical and non-analytical forms.