Following their initial collision 50--70 Myr ago, the Indian and Eurasian plates have been continuously converging toward each other. Whereas the regional stress field is predominately compressive, the Late Cenozoic tectonics within the Tibetan Plateau features widespread crustal extension. Numerous causes of the extension have been proposed, but their relative roles remain in debate. We have investigated the major factors contributing to the Tibetan extension in a three-dimensional viscoelastic model that includes both lateral and vertical variations of lithospheric rheology and relevant boundary conditions. Constrained by the present topography and GPS velocity field, the model predicted predominately extensional stress states within the plateau crust, resulting from mechanical balance between the gravitational buoyancy force of the plateau and the tectonic compressive stresses. The predicted stress pattern is consistent with the earthquake data that indicate roughly E-W extension in most of Tibet and nearly N-S extension near the eastern margin of the Tibetan Plateau. We explored the parameter space and boundary conditions to examine the stress evolution during the uplift of the Tibetan Plateau. When the plateau was lower than 50% of its present elevation, strike-slip and reverse faults were predominate over the entire plateau, and no E-W crustal extension was predicted. Significant crustal extension occurs only when the plateau has reached ~75% of its present elevation. Basal shear associated with underthrusting of the Indian plate beneath Tibet may have enhanced crustal extension in southern Tibet and the Himalayas, and a stronger basal shear during the Miocene may help to explain the development of the South Tibetan Detachment System.