This book presents the main results of extensive research on the diffraction, radiation and propagation of elastic waves in isotropic and anisotropic media and bodies of various shapes based on integral equations, the separation of variables, the method of Green's functions, the method of finite elements, and the method of boundary elements. It explores the application of methods and equations of the theory of diffraction to the problems of synthesis of hydroacoustic antennas, and considers the spatial characteristics of loudspeakers. The book also provides a detailed description of the acoustic monitoring of oil products in different volumes.