Abstract: The cause of welding residual stress and the principle of vibration stress relief for a pressure vessel were discussed. The wave vibration relief was put forward. The mechanism of wave vibration relief was analyzed from the dynamics aspect. Based on Flugge's shell equations, a method for calculating the eigen frequencies and modal solution was derived to the traveling-wave resonance response for a cylindrical shell. A speed formula for the rotating cylindrical shells at resonant frequency was obtained. Gauss method was exploited to calculate transcendental function of eigen frequency which can be solved with high accuracy. Calculation results of eigen frequency and axial wave stress were presented for a cantilever shell and mode shape was presented.