Magnitudes of differential stress in the lithosphere, especially in the crust, are still disputed. Earthquake-based stress drop estimates indicate median values <10 MPa whereas the lateral variation of gravitational potential energy per unit area (GPE) across significant relief indicates stress magnitudes of ca. 100 MPa in average across a 100 km thick lithosphere between the Indian lowland and the Tibetan plateau. These standard GPE-based stress estimates correspond to membrane stresses because they are associated with a deformation that is uniform with depth. We show here with new analytical results that lateral variations in GPE can also cause bending moments and related bending stresses of several hundreds of MPa. Furthermore, we perform 2-D thermomechanical numerical simulations (1) to evaluate estimates for membrane and bending stresses based on GPE variations, (2) to quantify minimum crustal stress magnitudes that are required to maintain the topographic relief between Indian lowland and Tibetan plateau for ca. 10 Ma and (3) to quantify the corresponding relative contribution of crustal strength to the total lithospheric strength. The numerical model includes viscoelastoplastic deformation, gravity and heat transfer. The model configuration is based on density fields from the CRUST1.0 data set and from a geophysically and petrologically constrained density model based on in situ field campaigns. The numerical results indicate that values of differential stress in the upper crust must be >ca. 180 MPa, corresponding to a friction angle of ca. 10° to maintain the topographic relief between lowland and plateau for >10 Ma. The relative contribution of crustal strength to total lithospheric strength varies considerably laterally. In the region between lowland and plateau and inside the plateau the depth-integrated crustal strength is approximately equal to the depth-integrated strength of the mantle lithosphere. Simple analytical formulae predicting the lateral variation of depth-integrated stresses agree with numerically calculated stress fields, which show both the accuracy of the numerical results and the applicability of simple, rheology-independent, analytical predictions to highly variable, rheology-dependent stress fields. Our results indicate that (1) crustal strength can be locally equal to mantle lithosphere strength and that (2) crustal stresses must be at least one order of magnitude larger than median stress drops in order to support the plateau relief over a duration of ca. 10 Ma.