This text considers computational techniques for the analysis of the dynamic fluid-structure interaction between a finite elastic structure and the associated acoustic field in the surrounding medium. Detailed attention is paid to almost all aspects of a complete solution to the fluid-structure interaction problem. Starting from the mathematical formulation, as partial differential equations, of the idealized problem, the text takes the reader through reformulation of the problem as boundary integral and variational equations, followed by a comprehensive study of their numerical solution by boundary and finite element methods, to details of actual experiments using sonar transducers in a test tank. The presentation is aimed at postgraduate students and researchers in engineering, science and mathematics who may be working in the areas of boundary integral methods, finite element methods, acoustics, and the fluid structure interaction.