Extensional deformation in the western United States, particularly in the Basin and Range, has frequently been ascribed to buoyancy forces arising from horizontal density contrasts. The Rio Grande rift is subject to buoyancy forces 2--3 times larger than those in the tectonically active northern Basin and Range, suggesting that it should be extending considerably faster than the northern Basin and Range, yet paradoxically is extending more slowly. Using a thin viscous sheet model, we test the hypothesis that regions surrounding the Rio Grande rift, which have rheologically stronger lithosphere, resist deformation and reduce the rate of extensional deformation in the Rio Grande rift to values consistent with observations. We find that these regions must have lithospheric strength at least twice that of the Rio Grande rift. This modest contrast in lithospheric strength is consistent with independent estimates derived from observations of heat flow, seismicity, and crustal thickness. ¿ 2001 American Geophysical Union