A Maxwell viscoelastic model is proposed for the lithosphere in the proximity of a long, vertical strike slip fault. In this framework, formulas for the recurrence time of great earthquakes are derived by imposing boundary conditions of (1) uniform strain rate in the fault region or (2) steady, aseismic sliding at depth. In both cases a minimum effective viscosity of the fault region is found in order that a critical stress for earthquake occurrence can be reached; at higher viscosities the recurrence time approaches a minimum, limiting value. Application of the model to the northern 'locked' segment of the San Andreas fault would indicate a recurrence time significantly longer than the often quoted 100-year period. These results differ considerably from those obtained from similar models employing boundary conditions of assigned stress at large distance from the fault.