The dynamics of shells of arbitrary geometry submerged in an acoustic medium has attracted attention for many decades. Only a finite region of the finite fluid domain can be modelled in the numerical analysis. The artificial surface encompassing the finite region is called the truncation surface, on which the transmitting boundary condition is used. The classical plane wave, cylindrical wave and spherical wave approximations are the first generation approximations. The residual variable method has made it possible to develop second generation improved transmitting boundary conditions in Cartesian, cylindrical and spherical coordinates. A general purpose finite element program, in which both the classical and improved transmitting boundary conditions have been incorporated, has been coded and verified. The response of a point excited submerged ellipsoidal shell is studied. The ellipsoidal shell is enclosed in a spherical truncation surface. The numerical results on the apex deflection are presented and they are compared with that of the spherical shell. (C) 1997 Civil-Comp Ltd and Elsevier Science Ltd.