Acoustic signals scattered from submerged elastictargets have produced interesting backscattered signals in the appropriate frequency region particularly because of the presence of resonances. Considerable work has been done for spherically and cylindrically shaped objects out to moderate frequencies for both solids and shells. Only recently, however, have researchers reported results for elongated objects such as spheroidal solids and shells. Further, the higher-frequency region for spheres has not been investigated extensively. A series of calculations that are characteristic of elongated targets or of spherical shells in the higher-frequency region are reported. Some of the discussed results involve bending resonances caused by obliquely incident plane waves on elongated objects and their relation to flexural resonances of beams; classes of resonances that are related to waves creeping along the longest and shortest meridians of a spheroid; flexural resonances (A0 resonances) for shells in the time domain near the coincidence frequency; and high-frequency thickness effects when scattering from shells, and their prediction based on flat plate theory. Several numerical examples are shown.