A nonlinear weighted least-squares inverse analysis was performed for a synthetic elastic layer over viscoelastic half-space model of strike-slip faulting, and an inversion of strain rate data was attempted for the locked portions of the San Andreas fault in California. The model parameters were: elastic layer thickness (H); fault locking depth (D); earthquake recurrence time (T); average shear modulus of the elastic layer and viscoelastic half-space (&mgr;); half-space viscosity (&eegr;); and coseismic offset (DU). Only the ratio of viscosity to shear modulus can be resolved, and thus shear modulus was held constant. Based on an eigenvector analysis of synthetic data, it is not possible to resolve all of the five remaining parameters with the current observations, which are very close to the fault and vary only with time since the last earthquake. A suite of inversions was therfore performed for the San Andreas, holding recurrence time and locking depth fixed at particular values for each inversion. These inversions resulted in nearly the same data misfit. Thus, a range of estimated values, rather than a particular set of values, was found for the remaining three parameters. Inversions on data from the northern San Andreas resulted in predicted parameter ranges similar to those produced by inversions on data from the whole fault. The addition of observations which vary with distance from the fault should help to constrain these ranges, and perhaps allow resolution of recurrence time and locking depth. ¿ American Geophysical Union 1988