A working hypothesis is developed for the two stages of evolution of the Tibetan plateau during the continental collision between India and Eurasia. The first phase was dominated by crustal shortening and thickening in what is now Tibet, while Indochina was expelled southeastward, away from Eurasia. At the end of this phase at 17 Ma, the estimated Tibetan crustal thickness was ~51 km. The second phase has been dominated by thickening of Tibet by the influx of crustal material from India, with no associated crustal shortening. The crustal thickening that is inferred to have occurred by this process is only feasible because leakage of crust from beneath the plateau is restricted by neighboring Archean cratons that block lower crustal flow. This leakage, to the east and south from Tibet to beneath Tunnan, is estimated as ~20--30% of the influx at present but was much smaller at the start of this second phase of deformation. It is suggested that at ~11 Ma the force exerted against the Tibetan upper crust by this flowing material first exceeded the threshold that this brittle layer could resist and Tibet began to extend eastward. Any satisfactory working hypothesis for the Tibetan plateau must explain its dimensions, its ~17 Ma ending of shortening and ~11 Ma start of extension and volcanism, the eastward slip sense on its active normal and strike-slip faults, and the ratios of their displacements to present-day slip rates, which imply that their slip rates have gradually increased. This working hypothesis accounts for these features and predicts a smooth and continuing increase in altitude. ¿ American Geophysical Union 1995