AbstractContinental‐scale glaciations cause deformation, geopotential, rotation and stress changes of the Earth. Subsurface stress changes have implications to future activities such as carbon capture and storage, enhanced oil recovery and deep geological disposal of nuclear waste. We model glacially induced stresses, strain changes and deformation for North America, with emphasis on the two potential sites for long‐term storage of used nuclear fuel in Canada (Saugeen Ojibway Nation (SON)‐South Bruce area in southwestern Ontario and Wabigoon Lake Ojibway Nation (WLON)‐Ignace area in northwestern Ontario). We apply a revised, high‐resolution ice history of the past glacial cycle from the University of Toronto Glacial Systems Model, assumed to be representative for future glacial cycles, together with a set of seven different one‐ and three‐dimensional earth structures. We find that glacially induced stresses and strains can vary strongly throughout a glacial cycle, whereas especially the horizontal components can change from tensional to compressive in nature. Such changes can happen within a few 1,000 years, caused by drastic and rapid ice thickness increase or decrease above the potential site. Despite SON‐South Bruce being located further away from the ice sheet center than WLON‐Ignace and temporarily in the forebulge of the developing ice sheet during glaciation, stresses and strains are very similar in magnitude and range at both sites. We also see the potential that the glacially induced stresses can alter the direction of the pre‐existing maximum horizontal stress at SON‐South Bruce. These results will be incorporated in the site safety and site selection process.