The areal extents of the Laurentide and Fennoscandian ice sheets during the Last Glacial Maximum (about 20,000 years ago) are well known(1), but thickness estimates range widely, from high-domed(2) to thin(3), with large implications for our reconstruction of the climate system regarding, for example, Northern Hemisphere atmospheric circulation and global sea levels. This uncertainty stems from difficulties in determining the basal temperatures of the ice sheets and the shear strength of subglacial materials(4), a knowledge of which would better constrain reconstructions of ice-sheet thickness. Here we show that, in the absence of direct data, the occurrence of ribbed moraines in modern landscapes can be used to determine the former spatial distribution of frozen- and thawed-bed conditions. We argue that ribbed moraines were formed by brittle fracture of subglacial sediments, induced by the excessive stress at the boundary between frozen- and thawed-bed conditions resulting from the across-boundary difference in basal ice velocity. Maps of glacial landforms from aerial photographs of Canada and Scandinavia reveal a concentration of ribbed moraines around the ice-sheet retreat centres of Quebec, Keewatin, Newfoundland and west-central Fennoscandia Together with the evidence from relict landscapes that mark glacial areas with frozen-bed conditions, the distribution of ribbed moraines on both continents suggest that a large area of the Laurentide and Fennoscandian ice sheets was frozen-based-and therefore high-domed and stable-during the Last Glacial Maximum.