The dynamic stability of thin shell with variable speed rotation is studied in this paper. Based on Donnell thin shell theory, vibration differential equation of cylindrical shell is established, which considers both variable speed and periodic axial force. The analytical expressions for boundaries of both primary and combined instability regions are derived by multiscale method. Variations of instability boundaries with excitation frequency and amplitude are discussed in three cases, i. e. , only periodic axial force, only variable speed rotation and both two time-varying factors. The analytical results are verified by comparing with literature results and numerical results.