The dynamics of crustal rifting in Iceland depend strongly on the lower crustal rheology, which controls the intensity of upper crustal stress concentration and scale time of heat diffusion from the underlying mantle plume. While magnetotelluric surveys suggest the presence of a pervasive hot and highly ductile lowermost crust with possibly high fraction of partial melt, observations of low seismic attenuation and strong shear wave transmission suggest a much cooler lower crust and upper mantle. Since viscosity is also sensitive to the degree of partial melt present, viscosity estimates for these regions could shed light on the factors responsible for these observations. In this study we utilize horizontal and vertical displacement vectors determined in GPS campaigns in northeast Iceland since 1986. These are modeled in terms of steady state tectonic loading plus postseismic/postdiking relaxation following the 1975--1984 Krafla rifting episode, as first proposed by Foulger and others. With the elastic part of the model fixed by external constraints, these data have a high sensitivity to the viscosity structure beneath Iceland. Lower crust and upper mantle viscosities of about 3¿1019 Pa s and 3¿1018 Pa s, respectively, yield the closest agreement with the data. Our lower crustal viscosity estimate is consistent with the low attenuation and low (subsolidus) temperature for the lower curst inferred in recent studies. Inversions for fissure opening during the Krafla rifting episode yield about 7 m of opening centered on the Krafla rift, as is observed. Allowing for contemporaneous deep rifting on vertical faults along the Askja segment partially accounts for the observed increase in separation across the rift during 1987--1992 but does not account for large displacements in the southeastern part of the network or the large relative subsidence around the Askja rift during in 1987--1990. Recent deep normal faulting beneath the Askja rift and further south might explain all of these remaining features. ¿ American Geophysical Union 1996