Site velocities from 349 Global Positioning System (GPS) stations are used to construct an 11-element quasi-rigid block model of the Tibetan Plateau and its surroundings. Rigid rotations of five major blocks are well determined, and average translation velocities of six smaller blocks can be constrained. Where data are well distributed the velocity field can be explained well by rigid block motion and fault slip across block boundaries. Residual misfits average 1.6 mm/yr compared to typical one standard deviation velocity uncertainties of 1.3 mm/yr. Any residual internal straining of the blocks is small and heterogeneous. However, residual substructure might well represent currently unresolved motions of smaller blocks. Although any smaller blocks must move at nearly the same rate as the larger blocks within which they lie, undetected relative motions between them could be significant, particularly where there are gaps in GPS coverage. Predicted relative motions between major blocks agree with the observed sense of slip and along-strike partitioning of motion across major faults. However, predicted slip rates across Tibet's major strike-slip faults are low, only 5--12 mm/yr, a factor of 2--3 smaller than most rates estimated from fault offset features dated by radiometric methods as ~2000 to ~100,000 year old. Previous work has suggested that both GPS data and low fault slip rates are incompatible with rigid block motions of Tibet. The results reported here overcome these objections.