Underwater acoustic studies of backscattering by submerged targets have generally focused on bodies with spherical and cylindrical symmetry. However, there are interests in scattering by objects which may be characterized by more angular features, with surfaces that tend to be composed of facets and edges. To investigate the scattering properties of such bodies, the backscattering by a number of elastic cubes, and irregularly shaped polyhedra, have been studied. Data were collected by measuring the band limited impulse response of the scatterers, using a broadband transducer, which operated as a transceiver, both transmitting and receiving signals. To present the scattering measurements nondimensionally a form function definition has been employed to normalize the backscattered signals. The normalized frequency has been expressed as ka, where k is the acoustic wave number, and a is a characteristic dimension of the scatterer. The cube observations covered a broad ka range, ka = 3–34, thereby encompassing the lower ka scattering region where the cube can be considered to be nominally rigid, through to higher ka values where it would be expected that the elastic properties of the cube become important. The measurements on irregular polyhedra are more limited in extent, however, the results are presented for comparison with the cube data. To compare the observations with predictions, computations of acoustic backscattering for both rigid and elastic cubes are presented.