We have examined a large set of dolphin-emitted acoustic pulses (`echolocation clicks') which were reflected from various elastic shells that were suspended, underwater, 4.5 m in front of the animal in a large test site in Kaneohe Bay. A carefully instrumented analog-to-digital system continuously captured the emitted clicks and also the returned, backscattered, echoes (A/D conversion at 500 kHz). Using standard conditioning techniques and food reinforces, the dolphin is taught to push an underwater paddle when the `correct' target--the one he has been trained to identify--is presented to him. He communicates to us his consistently correct identifying choices in this manner. We have examined many echoes returned by three types of cylindrical shells in both the time and frequency domains. We will show exactly how specific features observable in these displays are directly related to the physical characteristics of the shells. Our processing uses certain fundamental resonance principles to show which echo- features contain information about the size, shape, wall-thickness, and material composition of both the shell and its filler substance. In the same fashion that these resonance features give us the identifying characteristics of each shell, we believe they also give them to the dolphin. These echo features may tell him the target properties without any need for computations. We claim that this may be the fundamental physical explanation of the dolphin's amazing target-ID feats, upon which they base their recognition choices. Our claim may be substantiated by the detailed analysis of many typical echoes returned by various shells, when they are interrogated by several dolphins. Thus far, this analysis of many echoes from many shells has only been carried out for a single dolphin.