In southernmost California the Salton Trough sedimentary basin lies between the subparallel San Jacinto and San Andreas faults that together with the Elsinore fault, accommodate ~80% of the 50 mm/yr of Pacific--North American relative motion. The slip rates on the San Andreas and San Jacinto faults have been a matter of recent debate, and one source of uncertainty has been the influence of crustal strength heterogeneity due to elastically weak basin sediments on geodetic data. To evaluate these effects, we have modeled regional kinematics with elastic and viscoelastic finite element models that incorporate laterally and vertically varying crustal material properties. We find that in general, the effects of the sedimentary basin on surface deformation are relatively small and that to explain the geodetic velocity data, the slip rate on the San Andreas must be higher than that on the San Jacinto fault, consistent with traditional geologic estimates. We also conclude that a relatively strong lower crust of viscosity >5 ¿ 1019 Pa s exists in this region.