We have modeled the broad postseismic uplift measured by geodetic leveling in the epicentral area of the 1959 Mw = 7.3 Hebgen Lake, Montana earthquake, a normal faulting event in the northern Basin and Range province. To fit the observed uplift we calculate synthetic postseismic deformation using the relaxation response of a gravitational viscoelastic Earth to the earthquake. For a model with an elastic plate overlying a viscoelastic half-space, we find that the elastic thickness is 38 ?? 8 km, which isclose to the local crustal thickness. The half-space viscosity is estimated at 4 ?? 1018??0.5 Pa s. The leveling data do not require a viscous lower crust but permit a lower bound viscosity of 1020 Pa s. The observed broad uplift cannot be explained by physically plausible afterslip on and below the coseismic fault. However, local deformation across the coseismic surface rupture requires shallow afterslip reaching the surface. The postseismic deformation induced by the estimated viscoelastic structure decays exponentially with a time constant of ???15 years. Because of coupling between the elastic layer and the viscoelastic substrate, this relaxation time is significantly longer than the 2 year Maxwell relaxation time of the viscous half-space itself. Our result suggests the importance of postseismic relaxation in interpreting high-precision global positioning system velocities. For example, our model results suggest that postseismic transient velocities from both the 1959 Hebgen Lake and the 1983 Mw = 6.9 Borah Peak earthquakes are currently as large as 1-2 mm/yr.