Theoretical and experimental studies indicate that when oceanic crust is hotter than about 800¿C, variations in crustal thickness drive lower crustal flow. We investigate the nature of crustal flow beneath Iceland, where zero-age crust varies in thickness from under 20 km to over 40 km over a distance of 100 km and temperatures exceed 1000¿C below depths of a few kilometers. We model the regional characteristics of crustal flow using the two-dimensional channel flow equation with depth-dependent viscosity. The model predicts the observed decay in crustal thickness contrasts between zero-age and off-axis crust on shore Iceland and development of a sharp Moho step as the plate moves away from the rift axis. These features become locked in place as plate cooling increases the viscosity. Observations are best matched by model predictions when the solidus viscosity is of order 1018 Pa s, in agreement with viscosity estimates from deformation rates associated with deglaciation and plate boundary processes. Crustal flow acts to erase the crustal thickness memory of ridge-plume interaction, so that maps of Icelandic crustal thickness can be used neither to derive a detailed plume flux history nor to test in detail whether the Iceland Plume center is fixed relative to other hot spots. Crustal flow beneath Iceland is an unusually clear example of the kind of flow postulated to explain continental phenomena including exhumation of metamorphic core complexes and associated development of low-angle detachments within extensional terrains and sharp-edged plateau topography in major collisional belts.