The topography of the sea floor between Iceland and Jan Mayen Island is flat and elevated in relation to most ocean basins. Marine geophysical observations in the area have shown that it was formed by sea floor spreading but have not revealed details of structures more than a few hundred meters beneath the sea floor. We have examined the dispersion of seismic surface waves across the Iceland Plateau and have modeled structures to depths of up to 100 km. We find that the thickness of the crustal component of the lithosphere is much greater than that of normal oceanic structures, perhaps exceeding 20 km. We suggest that the elevation of the region is due to isostatic compensation for this excess of low-density crustal material. The total lithospheric thickness is about 50 km throughout the region, indicating that the lithosphere thickens with age at a rate similar to that found in other young oceans.