Abstract: A complex analysis is made to study the linear wavy vibration of a cantilever rotating thin cylindrical shell under the action of a normal exciting force with damping taken into account, based on Donnell's theory of cylindrical shell. The results show that the complex analysis is available to solve the problem of such rotating wavy vibration. In the solution the condition that the real parts of both forward and backward traveling waves are equal to zero can be used to determine the frequencies and rotating speeds of resonance, while the virtual parts can determine the response values. There are two resonance frequencies when the rotating thin cylindrical shell vibrates linearly. The response curve of the wavy vibration is a beat-frequency one and its amplitudes relate to the damping ratio in wave mode. In general, the resonance amplitude of backward traveling wave is bigger than that of forward traveling wave.