The inverse problem of diffraction of elastic waves by the edge of a large crack has been investigated on the basis of elastodynamic ray theory and the geometrical theory of diffraction. Two methods are discussed for the mapping of the edge of a crack-like flaw in an elastic medium. The methods require as input data the arrival times of diffracted ultrasonic signals. The first method maps flash points on the crack edge by a process of triangulation with the source and receiver as given vertices of the triangle. By the use of arrival times at neighboring positions of the source and/or the receiver, the directions of signal propagation, which determine the triangle, can be computed. This inverse mapping is global in the sense that no a priori knowledge of the location of the crack edge is necessary. The second method is a local edge mapping which determines planes relative to a known point close to the crack edge. Each plane contains a flash point. The envelope of the planes maps an approximation to the crack edge. The errors due to inaccuracies in the input data and in the computational procedure have been illustrated by specific examples.