In Southeast Alaska extreme uplift rates are primarily caused by Glacial Isostatic Adjustment (GIA), as a result of ice load changes from the Little Ice Age to the present combined with a low viscosity asthenosphere. Current GIA models adopt a one-dimensional (1D) stratified Earth structure. The three-dimensional (3D) structure of the Earth is complex in this region due to the proximity of a subduction zone and the transition from a continental to oceanic plate. A simplified 1D Earth model may not be an accurate representation in this region and therefore affect the GIA predictions. In this study a numerical model for 3D GIA is constructed for Southeast Alaska. We present an assessment on the impact of lateral variations in the upper mantle rheology on the vertical GIA component. We test two different approaches to obtain a 3D viscosity structure in the upper mantle. For the first approach, viscosities are inferred from lateral variations in temperature through flow laws for olivine. The water and grain size are varied to find a viscosity structure that best fits the GPS data. We find a best-fit viscosity structure with wet rheology (400 wt ppm H₂O) and grain size 8 mm. However, this model does not perform better (in terms of Χ²) than a radially symmetric model, because predicted uplift rates are much lower than the observed values. For the second approach, we infer a viscosity distribution obtained directly from shear wave anomalies through scaling relationships. Our 3D model reduces the residuals between 1.0-2.7 mm/yr. We find that the effects of lateral variations in viscosity (up to 0.4 log units or, equivalently, a factor of 2.5) are in principle detectable by the GPS network and provide a better overall fit than a radially symmetric 1D viscosity model.