Shortly after the excavation of a large impact crater the transient cavity collapses, driven by gravity. We show that at least one concentric fault scarp forms about the crater if the strength of the target material decreases sufficiently rapidly with increasing depth. This is demonstrated by two classes of models: extrusion flow models which assume a weak layer underlying a strong layer, and plastic flow models which assume a continuous decrease of cohesion strength with depth. Both classes predict that the ratio of the radius of the scarp to the transient crater radius is between 1.2 and 2 for large craters. The surface cohesion strengths needed in the plastic collapse models are consistent with those required by previous work on the slumping of small(ca. 15km diameter) craters.