[1] A broad uplift occurs in Iceland in response to the retreat of ice caps, which began circa 1890. Until now, this deformation signal has been measured primarily using GPS at points some distance away from the ice caps. Here, for the first time we use satellite radar interferometry (interferometric synthetic aperture radar) to constrain uplift of the ground all the way up to the edge of the largest ice cap, Vatnajökull. This allows for improved constraints on the Earth rheology, both the thickness of the uppermost Earth layer that responds only in an elastic manner and the viscosity below it. The interferometric synthetic aperture radar velocities indicate a maximum displacement rate of 24AE4 and 31AE4 mm/yr at the edge of Vatnajökull, during 1995Vatnajökull, during -2002Vatnajökull, during and 2004Vatnajökull, during -2009, respectively. The fastest rates occur at outlet glaciers of low elevation where ice retreat is high. We compare the observations with glacial isostatic adjustment models that include the deglaciation history of the Icelandic ice caps since 1890 and two Earth layers. Using a Bayesian approach, we derived probability density functions for the average Earth model parameters for three satellite tracks. Based on our assumptions, the three best fit models give elastic thicknesses in the range of 15-40 km, and viscosities ranging from 4-10Â 10 18 Pa s.