The origin of the southern California uplift is investigated using models in which the viscoelastic properties of the asthenosphere and the fluid flow (poroelastic) properties of the upper lithosphere are accounted for. The uplift is presumed to be a recurrent process related to the compressional tectonics of the Transverse Ranges, which have been elevated as much as 3 km in Quaternary time. The uplift itself is modeled by aseismic slip at depth on a thrust fault dipping at a shallow angle. Introducing stress relaxation properties in the lithosphere and asthenosphere causes subsequent time-dependent deformation. In the case of asthenospheric relaxation, the post-slip movements involve further elevation of the uplifted region and approximately north-south oriented tensional strains, both of which disagree to some extent with observations. Poroelastic relaxation is simulated by abruptly decreasing the elastic moduli in the upper lithosphere once fault slip has ceased. The result is subsidence of previously uplifted regions and continued north-south contractional straining. Although these features qualitatively agree with observations, the success of the model is mixed. Matching the measured partial collapse requires a large (factor of 3) elastic modulus change in the upper crust, introducing possible large changes in seismic wave velocities which are not observed. Whether these defects eliminate fluid flow as a mechanism for the partial collapse or merely reflect the shortcomings of an overidealized model is not yet clear.