We investigate numerically the evolution of crustal and lithospheric thickness, thermal structure, topography, and strain rate of the Tibetan Plateau through time, using the thin viscous sheet approach. We show that lithospheric mantle must have been removed from beneath Tibet to explain the present surface elevation and lack of regional surface slope. In the absence of this removal, the modeled topography reaches a maximum elevation of <4000 m (for weak rheology), or the surface slopes significantly northward (for strong rheology). The crust must have been warmed and weakened by an increase of radiogenic heat production at depth due to crustal thickening. In the absence of this warming, viscous stresses associated with plate convergence exceed stresses produced by topography, and the present pattern of vertical thinning and east-west extension would not have developed. Continuous removal of lithosphere, by delamination or convection, does not allow sufficient crustal warming and fails to reproduce either the present topography or the pattern of active deformation on the plateau in a reasonable time. Geologically rapid removal of the lithospheric root beneath the thickened crust of Tibet successfully explains the current elevation of the plateau, its lack of surface slope, the steep south and north margins, and the pattern of the present deformation, including vertical thinning, E-W extension, and extrusion and vertical axis rotation on the eastern margin. Our modeling suggests that this removal took place within the last 12 m.y.