During the first 2 years following the 2002 Mw = 7.9 Denali, Alaska, strike-slip earthquake, a large array of Global Positioning System (GPS) receivers recorded rapid postseismic surface motions extending at least 300 km from the rupture and at rates of more than 100 mm/yr in the near field. Here we use three-dimensional (3-D) viscoelastic finite element models to infer the mechanisms responsible for these postseismic observations. We consider afterslip both from an inversion of GPS displacements and from stress-driven forward models, poroelastic rebound, and viscoelastic flow in the lower crust and upper mantle. Several conclusions can be drawn: (1) No single mechanism can explain the postseismic observations. (2) Significant postseismic flow below a depth of 60 km is required to explain observed far-field motions, best explained by a weak upper mantle with a depth-dependent effective viscosity that ranges from >1019 Pa s at the Moho (50 km depth) to 3--4 ¿ 1018 Pa s at 100 km depth. (3) Shallow afterslip within the upper crust occurs adjacent to and beneath the regions of largest coseismic slip. (4) There is a contribution from deformation in the middle and lower crust from either lower crustal flow or stress-driven slip. Afterslip is preferred over broad viscoelastic flow owing to the existence of seismic velocity discontinuities across the fault at depth, though our modeling does not favor either mechanism. If the process is viscoelastic relaxation, the viscosity is a factor of 3 greater than the inferred mantle viscosity. (5) Poroelastic rebound probably contributed to the observed postseismic deformation in the immediate vicinity of the Denali/Totschunda junction. These conclusions lead us to infer an Alaskan mechanical lithosphere that is about 60 km thick, overlying a weak asthenosphere, and a Denali fault that cuts through the entire lithosphere with shear accommodated by faulting in the top ~20 km and time-dependent aseismic shear below.