Abstract: Based on the linear differential equations of motion of missile body with variable parameters, the present paper has developed the stability criterion of the free motion of missile body with variable parameters having sufficient conditions, using Lyapunov stability theory. On this basis and using Popov,s superstability theory, the stability criterion of the free pitch or yaw motion fora missile body satisfying the sufficient and necessary conditions have also been developed. These criteria can be applied to the motion stability analysis and the design of rotating or non-rotating missile bodies. Some results of the criteria can also be applied to the motion stability analysis and design of uncontrolled rockets.