The deformation of the earth's surface immediately following an earthquake is well modeled by a dislocation in an elastic half space. Some time after the event, however, the elastic stresses begin to relax due to flow in the more fluid regions of the upper mantle (the asthenosphere). This relaxation causes further slow displacements observable at the earth's surface. This paper examines the pattern and timing of these postseismic motions for a vertical dip slip fault and a 30¿ dip thrust fault. A variety of rheological models are studied. These models encompass variations in asthenosphere thickness, mesosphere viscosity, fault depth, and most important, power law flow. Both Newtonian (n=1) and non-Newtonian (n=3) Maxwell rheologies are considered for the asthenosphere and mesosphere. The results for a vertical dip slip fault show that a peripheral upwarp develops within a distance of a few lithosphere thicknesses from the rupture zone on the downthrown side of the fault (a comparable downwarp develops on the upthrown side). These peripheral warps grow to a maximum height of about 5% of the total fault slip some time after the earthquake event and then collapse at much greater times. The vertical motions for a 30¿ dip thrust fault show that after the earthquake a general uplift occurs in the region near the rupture zone. Horizontal displacements propagate asymmetrically away from the rupture zone, the largest displacements occurring in the overthrust plate. The principal result of the comparison of n=1 and n=3 rheological laws is that the basic pattern of uplifts and horizontal motions is very similar: the major difference is the time dependence of the development of the pattern. In spite of the complex geometrical structure of the subduction zone the displacements ui(1)(t) for Newtonian rheology are nearly the same as ui(3)(t') for the non-Newtonian rheology if t'~t3. Thus although the qualitative pattern of the displacements is not diagnostic of power law flow, the great difference in time dependence allows a clear discrimination of the two flow laws.