The lateral stability of a gliding parachute or other lifting surface with a suspended payload is analyzed to determine the relationship of aerodynamic and inertial parameters to stability characteristics. The system is represented by a rigid wing with a suspended payload in a steady glide. As with conventional fixed-wing aircraft, the lateral response is characterized by an oscillatory response mode and a spiral divergence. The stability boundary for spiral divergence can be prescribed analytically. Calculations show that there is a minimum effective anhedral angle required for absolute stability. Increasing suspension line length is stabilizing for spiral divergence, whereas increasing the glide slope is stabilizing for both spiral divergence and oscillatory response.