Abstract: A new 6DOF (six degree of freedom) two-axle automobile multi-body handling stability model was developed by the Roberson-Wittenburg method. In the model, a suspension system was taken into account. On this base, automobile handling stability was analyzed further by the Hurwitz theorem. The results show that an automobile with nice stable ride performance should follow two necessary conditions:the product of the square of rear bearing spring effective range and the rear suspension single side spring constant should be more than that of the square of front bearing spring effective range and the front suspension single side spring constant; the product of the mass hold by rear axle and the front tyre lateral stiffness should be more than the product of the mass hold by front axle and the rear tyre lateral stiffness. The second condition complements the deduced condition from a classic 2DOF automobile handling stability model.