This report presents a numerical technique for the linear dynamic analysis of a finite elastic structure immersed in an infinitie homogeneous acoustic medium. A finite element analysis of the structure is matched at the structure-fluid interface with an integral equation representation of the exterior acoustic field, leading to a coupled system of equations which may be cast in either acoustic or structural form. The former approach is preferred here for which numerical results are presented when the method is applied to plane wave scattering by thick and thin elastic spherical shells. (Author)