We construct a viscoelastic cycle model of plate boundary deformation that includes the effect of time-dependent interseismic strain accumulation, coseismic strain release, and viscoelastic relaxation of the substrate beneath the seismogenic crust. For a given fault system, time-averaged stress changes at any point (not on a fault) are constrained to zero; that is, kinematic consistency is enforced for the fault system. The dates of last rupture, mean recurrence times, and the slip distributions of the (assumed) repeating ruptures are key inputs into the viscoelastic cycle model. This simple formulation allows construction of stress evolution at all points in the plate boundary zone for purposes of probabilistic seismic hazard analysis (PSHA). Stress evolution is combined with a Coulomb failure stress threshold at representative points on the fault segments to estimate the times of their respective future ruptures. In our PSHA we consider uncertainties in a four-dimensional parameter space: the rupture peridocities, slip distributions, time of last earthquake (for prehistoric ruptures) and Coulomb failure stress thresholds. We apply this methodology to the San Francisco Bay region using a recently determined fault chronology of area faults. Assuming single-segment rupture scenarios, we find that fature rupture probabilities of area faults in the coming decades are the highest for the southern Hayward, Rodgers Creek, and northern Calaveras faults. This conclusion is qualitatively similar to that of Working Group on California Earthquake Probabilities, but the probabilities derived here are significantly higher. Given that fault rupture probabilities are highly model-dependent, no single model should be used to assess to time-dependent rupture probabilities. We suggest that several models, including the present one, be used in a comprehensive PSHA methodology, as was done by Working Group on California Earthquake Probabilities.