The acoustic scattering that results when penetrable underwater targets are insonified by transient waveforms is studied. The targets are various elastic shells—and also a rigid sphere for comparison—of several thicknesses that are described either exactly by the equations of three‐dimensional elasticity, or approximately by means of Donnell's shell theory. Significant signal processing parameters are outlined that are useful at the source, at the target, and at the receiver to predict quantitatively the nature of the entire scattering process taking place around a submerged structure. These parameters play an important role in the ultimate goal of active target identification [cf. G. Gaunaurd, J. Acoust. Soc. Am. Suppl. 185, S134 (1989)]. This approach, which exploits similarities with the radar literature, is first introduced here for targets away from environmental boundaries and in noiseless media. One should first know what type of echoshouldone receive from a sonartarget, before such return is corrupted and distorted by the environment. The idealized situation described here already uses much of the machinery of statistical communication theory (viz., matched filters, correlations and ambiguity functions, etc.) and is well suited for later extensions to cases accounting for high noise levels and for proximity to boundaries. The pertinent quantities are illustrated with many computed displays related to: (a) the incident pulses; (b) the targets themselves; and (c) the backscattered pulses.