It is well known that geodetic data from a single instant in time cannot uniquely characterize structure or rheology beneath active seismogenic zones. Nevertheless, comparison of spatial and temporal variations in deformation rate with time-dependent mechanical models can place valuable constraints on fault zone geometry and rheology. We consider postseismic strain rate transients by comparing geodetic data from north of San Francisco Bay obtained between 1906 and 1995 to predictions from viscoelastic finite element models. Models include (1) an elastic plate over a viscoelastic half-space, (2) distributed shear within a viscoelastic layer, (3) discrete shear zones within an otherwise elastic layer, (4) discrete shear zones in combination with distributed viscoelastic shear, and (5) midcrustal detachment surfaces. We vary, as applicable, locking depth, elastic thickness, depth to the top and bottom of the distributed shear layer, distributed shear relaxation time, discrete shear zone relaxation time, and discrete shear zone width. The best fitting, physically reasonable elastic plate over viscoelastic half-space models (1) do a poor job simultaneously predicting spatial and temporal variations in the data. The best fitting distributed shear models (2) do a poor job predicting spatial variations in the deformation rate. Although they fit the geodetic data, recent findings from seismic reflection-refraction studies in northern California argue against models with shallow subhorizontal detachments (5). Models incorporating discrete shear zones (3, 4) provide the best fit to the geodetic data and are consistent with seismic studies that argue for discrete fault zones extending through the entire crust.