Spinning cylindrical shells are critical components in practical engineering structures. The boundary conditions at the shell ends are diverse and significantly influence the vibration characteristics of the shell. To study these characteristics under vari? ous boundary conditions， a dynamic model of the spinning cylindrical shell is established using Lagrange equations and Novozhilov’s shell theory. The mathematical description of the boundary conditions for the cylindrical shell is combined with the discretized dis? placement functions， which are constructed based on a linear combination of Chebyshev polynomials. These functions satisfy the boundary conditions and are independent of the cylindrical shell's parameters. The vibration characteristics of stationary cylindrical shells are determined by solving the eigenvalue problems， revealing the influence of rotary inertia on the vibration characteristics. The applicability of different shell theories with respect to various geometrical parameters of the shell is discussed. Additionally， cir? cumferential wave-dependent mode functions are identified and used to compute the natural frequencies of shell modes with the zero circumferential waves， as well as the travelling waves of the spinning cylindrical shell under different boundary conditions. The im? pact of structural parameters on the natural frequencies of the travelling waves is also analyzed.