An analytical technique for the evaluation of combustion stability in rocket motors with partial length acoustic liners is presented. The combustors considered in this work have concentrated combustion zones at the injector, finite mean flows, cylindrical cross sections, and acoustic liners of arbitrary length and impedance. Linear three dimensional oscillations in such combustion chambers are analyzed using an integral equation-iteration technique. Stability limits in terms of the sensitive time lag model are calculated for several values of Mach Number, length to radius ratio, liner impedance, liner length, liner location, and nozzle admittance. Results indicate that increasing liner length increases combustor stability substantially at low Mach Numbers but has a considerably smaller effect for larger Mach Numbers. Increasing Mach Number or length to radius ratio has a destabilizing effect while liner location has only a minor effect on stability.