We use new models of crustal structure and the depth of the lithosphere–asthenosphere boundary to calculate the geopotential energy and its corresponding geopotential stress field for the High Arctic. Palaeostress indicators such as dykes and rifts of known age are used to compare the present day and palaeostress fields. When both stress fields coincide, a minimum age for the configuration of the lithospheric stress field may be defined. We identify three regions in which this is observed. In north Greenland and the eastern Amerasia Basin, the stress field is probably the same as that present during the Late Cretaceous. In western Siberia, the stress field is similar to that in the Triassic. The stress directions on the eastern Russian Arctic Shelf and the Amerasia Basin are similar to that in the Cretaceous. The persistent misfit of the present stress field and Early Cretaceous dyke swarms associated with the High Arctic Large Igneous Province indicates a short-lived transient change in the stress field at the time of dyke emplacement. Most Early Cretaceous rifts in the Amerasia Basin coincide with the stress field, suggesting that dyking and rifting were unrelated. We present new evidence for dykes and a graben structure of Early Cretaceous age on Bennett Island.