Leveling, Global Positioning System, very long baseline interferometry, and tide gauge observations indicate that time-dependent uplift has occurred on the Kenai Peninsula and adjacent regions of southern Alaska that subsided coseismically in the 1964 Prince William Sound earthquake. These observations have been critically assessed and used along with seismological and geological information as constraints in various aseismic slip and viscoelastic flow models of crustal deformation. The postseismic uplift rate in most of the region is significantly greater than the expected interseismic average. Some, but not all, of the data indicate that the uplift rate was quite rapid (more than several centimeters per year) in the years immediately following the earthquake and has slowed to a few centimeters per year or less since then. The modeling shows that the uplift can be explained by aseismic slip at depth but not by viscoelastic flow. The slip at depth since 1964 must have a transient as well as a steady component, since the deduced slip is considerably greater than the roughly 1.5 m expected from North American-Pacific plate convergence since the 1964 event. The minimum amount of slip required to fit the observations comes from an elastic model and is about 2.75 m. Viscoelastic models require more slip, since the dominant effect of viscoelastic flow is to produce subsidence in the region that is uplifted. A simple parameterization of the transient component using an amplitude and decay time is adequate to explain the observations. While the parameters deduced from the viscoelastic models have some ambiguity, the viscosity of models that best fit the observations cannot be much less than several times 1019 Pa s when the thickness of the North American plate is taken to be about 90 km.