Topography extracted from swath profiles along the northern, southern, and eastern margins of the Tibetan Plateau show two end-member morphologies: steep, abrupt margins and long-wavelength, low-gradient margins. Because the lack of significant upper crustal shortening across much of the eastern plateau margin implies that the crustal thickening occurs mainly in the deep crust, we compare regional topographic gradients surrounding the plateau to model results for flux of a Newtonian fluid through a lower crustal channel of uniform thickness. For an assumed 15-km-thick channel, we estimate a viscosity for the lower crust of 1018 Pa · s beneath the low-gradient margins, 1021 Pa · s beneath the steep margins, and an upper bound of 1016 Pa · s beneath the plateau. These results indicate that the large-scale morphology of the eastern plateau reflects fluid flow within the underlying crust; crustal material flows around the strong crust of the Sichuan and Tarim Basins, creating broad, gentle margins, and “piles up” behind the basins creating narrow, steep margins. These results imply that this portion of the Eurasian crust was heterogeneous, but largely weak, even prior to construction of the Tibetan Plateau.