John G. Harris intended to explain in this book the special techniques required to model the radiation and diffraction of elastic and surface waves. Sadly, he died before he could fulfil this ambition, but his plan has been brought to fruition by a team of his distinguished collaborators. The book begins with the basic underlying equations for wave motion and then builds upon this foundation by solving a number of fundamental scattering problems. The remaining chapters provide a thorough introduction to modern techniques that have proven essential to understanding radiation and diffraction at high frequencies. Graduate students, researchers and professionals in applied mathematics, physics and engineering will find that the chapters increase in complexity, beginning with plane-wave propagation and spectral analyses. Other topics include elastic wave theory, the Wiener-Hopf technique, the effects of viscosity on acoustic diffraction, and the phenomenon of channelling of wave energy along guided structures.