Abstract: The vehicle would have a dynamic response process in aerodynamics under a rudder deflecting manipulation. However, this dynamic process is often ignored in current research about the characteristics of rudder manipulation and only the static characteristics such as the rudder's inversed effect and control efficiency are taken into account. It is focused in this paper the dynamic response process about a supersonic maneuvering aircraft under the rudder manipulation. A dynamic mesh technique and unsteady numerical methods are developed to simulate the relative motion between the rudder and the aircraft body and the dynamic responses. Supersonic flow about a square cross-section missile and the flow about a forced pitching airfoil are simulated to verify the numerical methods. Then the rudder manipulation processes of the square cross-section missile under the three generic rudder deflection types (step-type, pulse-type and sinusoid-type) are simulated, and dynamic response of the missile's pitching motion under the rudder control is obtained. The results indicate that a fast rudder control process can even cause instability in the pitching motion of the missile.