Models of viscous crater relaxation proposed to date for the icy satellites of the outer solar system assume the behavior of a Newtonian medium, with viscosity &eegr; independent of effective stress &tgr;. While this is reasonable of both effective stresses and temperatures are very low, laboratory data on ice indicate that, at effective shear stresses (&tgr;~0.1 MPa) and temperatures (~173 K) likely to occur in regions underlying craters, non-Newtonian behavior is probable. Such material would have a viscosity-effective stress relation given by &eegr;(&tgr;) ∝&tgr;1-n, where n≈4. It is likely, due to the low activation energy of ice at these temperatures, that stress differences may affect the profile of relaxing craters to a greater extent than temperature differences. To investigate the effects of a non-Newtonian rheology on the profiles of relaxing craters, two-dimensional finite element simulations have been performed. Initially, effective stresses are highest in the region below the crater center, producing a zone of relatively low viscosity. Relaxation flow forces this region into a convex bulge as the crater relaxes. At later stages, the low viscosity region moves to beneath the crater rim, leading to enhanced relaxation of crater rims, compared to a Newtonian rheology. The reduction of effective stress as the crater relaxes increases viscosity in the region beneath the crater. As a result, relaxation rates are quite rapid compared to those in later stages. This is in marked contrast to the exponential behavior of depth with time associated with Newtonian relaxation. The short relaxation times observed for the craters modeled indicate that a silicate component may be required in the crusts of icy satellites to account for the observed crater populations. ¿ American Geophysical Union 1987