Previous studies of the title problem have produced only partial solutions for this classical configuration. The present study shows how complete solutions are readily obtained from simple polynomial expressions. Numerical results in graphical form are presented for a steel shell submerged in water as functions of a parameter related to the shell’s thickness‐to‐radius ratio. It is found that descriptions based upon added‐mass and added‐damping perturbations of the shell’sinvacuofree‐vibration characteristics can be misleading.