Active sonar classification of submerged elastic structures becomes increasingly difficult when the structure is close to the bottom or surface of the sea. The backscattering cross-section (BSCS) of any target, which is relatively simpler to determine in deep waters, away from boundaries, becomes substantially distorted as the structure approaches either one of these environmental boundaries. Near these interfaces the classification methodology based on echo resonances that we have used in the past (viz., Appl. Mechanics Reviews 43, 171-208, (1990)) can no longer be used. By means of the examples of a spherical shell and an elastic solid sphere insonified by plane waves, we study the above mentioned degradation in BSCS in order to assess how distant the structure should be from these boundaries before the resonance features become discernible again in the echoes, and object recognition is again possible. Our approach is based on the method of images for the construction of the appropriate Green's functions, combined with a very involved two-body scattering formulation that determines the combined T-Matrix of two insonified objects, when the T-Matrix of each individual object is known. The method is extended to the time domain. We present form-functions in the frequency domain, as well as late-time responses in the time domain for both sphere and shell as they approach the mentioned boundaries. Boundary effects seem to be confined to a 'skin layer' bounded by R <EQ 4. Within this layer the resonance features fade and are washed out in both the frequency and time domains. The formulation uses translation operators borrowed from atomic physics.