Vibrational energy flow model of ABH cylindrical shells with arbitrary profile and general boundary conditions is established using Rayleigh-Ritz method in conjunction with improved Fourier series expansion. Energy equation based on Love’s shell theory is formulated, while the ABH cylindrical shells including any type of indentation profile can be considered uniformly and invariantly expanded into Fourier series accordingly. The vibrational displacements are expanded with the modified version of Fourier series. The proposed model is validated through the comparisons with experimental results and those calculated from finite element method, and excellent agreement can be observed. The power flow analysis illustrates that the vibrational energy flow into ABH indentations is intensified and absorbed by damping materials compared with that of the uniform one for nearly all the frequency ranges. However, the energy absorption loses efficacy in certain low frequencies, which are coincided with its overall mode shapes. This work can shed some new light on the vibration behavior study of ABH cylindrical shell from the viewpoint of energy transmission, and can provide an efficient analysis tool for the vibration characteristics study and its optimal design of such complex structural system embedded with Acoustic Black Holes.