An elastic finite-element analysis of the African intraplate stress field is used to determine constraints on the stress state resulting from variations in the gravitational potential energy of the lithosphere (U1) produced by lateral density variations. The modeling is constrained by 150 stress indicators extracted from the World Stress Map Project data set. Lateral variations in U1 are calculated by using a simple lithospheric density model that is consistent with observed geoid anomalies across mid-ocean ridges and continental margins. Predicted tectonic stresses in the oceanic regions of the African plate range from tension along the mid-ocean ridges (9 MPa) to compression in the ocean basins (10 MPa). Continental regions near sea level are in a near-neutral state of stress. There are large extensional stresses present in the Ethiopian highlands (15 MPa), the East African rift (9 MPa), and southern Africa (8 MPa). The general agreement between the predicted and the observed stress fields suggests that the principal long-wavelength features of the intraplate stress field, including the observed extension in eastern and southern Africa, can be explained in terms of stresses arising from lithospheric density variations without appeal to poorly determined sublithospheric processes. The state of stress in continental regions with elevations greater than 70 m is predicted to be extensional, providing an alternative source of continental tension that has important implications for the dynamics of continental breakup.