It is well known that slip rate estimates from geodetic data are nonunique because they depend on model assumptions and parameters that are often not known a priori. Estimates of fault slip rate on the Mojave segment of the San Andreas fault system derived from elastic block models and GPS data are significantly lower than estimates from geologic data. To determine the extent to which the slip rate discrepancy might be due to the oversimplified models of the rheology of the lithosphere, we develop a two-dimensional linear Maxwell viscoelastic earthquake cycle model and simultaneously estimate fault slip rates and lithosphere viscosity structure in the Mojave region. The model consists of episodic earthquakes in an elastic crust overlying layers with different viscosities that represent the lower crust, uppermost mantle, and upper mantle. We use GPS measurements of postseismic relaxation following the 1992 Landers earthquake, triangulation measurements spanning 1932–1977, GPS measurements of the contemporary velocity field, and paleoseismic data along the San Andreas fault. We infer lower crustal (15–30 km depth) viscosity of ∼1019–1020 Pa s, uppermost mantle (30–60 km) viscosity of ∼1020–22 Pa s, and underlying upper mantle viscosity of ∼1018–1019 Pa s, consistent with inferences from laboratory experiments of relatively high-viscosity lithospheric mantle and lower-viscosity lower crust and underlying asthenospheric mantle. We infer a 20–30 mm/yr slip rate on the San Andreas fault, in agreement with the lower end of geologic estimates. Inversions of geodetic data with models that do not incorporate layered viscosity structure may significantly misestimate slip rates.