This paper explores theoretically the possibility of using caustics, formed in the ultrasonic field diffracted by defects, as an approach to the inverse scattering problem, The case of crack-like defects is considered in detail, using the geometrical theory of diffraction. The involute of the far field caustic reproduces the projection of the crack edge in the incident beam direction, for a plane incident wavefront. This purely geometrical inversion is carried out uniquely for the astroid and its involute, the elliptical edge. For a general edge shape, the complete inversion requires one further length measurement, which may be carried out in some cases by further experiments with caustics, Usefullimitations on the possible shapes of caustics are explained on the basis of catastrophe theory, Calculations show that the inherent intensity-level change (~2-3 dB) and width ( ~ wavelength) over which it occurs for a typical ultrasonic caustic are adequate for observation. Some discussion is given of experimental requirements, as well as of caustics formed in the near field of a crack and of those formed by voids and inclusions. The topology of the far field caustic cannot in general distinguish between volumetric and crack-like defects. Studying caustics may prove to be a useful adjunct to ultrasonic imaging systems for the inspection of fatigue cracks.