In order to deal with the vibration problem about machinery installed in a cylinder, the analytical model for a single-stage passive isolation system which consists of complex excitations, multiple elastic mounts and a circular cylindrical shell foundation is established. Based on classical thin shell theories and modal superposition principle, the mobility functions of a cylindrical shell with both ends shear diaphragms supported are derived. In these expressions, the responses of odd and even modes are taken into account together. The mobility matrix is used to characterize the relationship between different forms of forces and speed responses. Wave effects in elastic mounts are considered also, and the mobility method is applied to derive the power flow transfer equations of the overall system. It is found that the standing longitudinal and flexural waves of the mounts induced by the vertical force, transverse force and moment excitations have obvious effects on the power transmission at high frequencies. Moment excitation has an important effect on the transmission of power into the flexible cylinder. It necessarily suggests that the radial flexural vibration component plays a dominant role in the power transmission. This proposed approach is provided with modular scalability and can provide a theoretical guidance for the structural parameter optimization and integrated passive and active control strategies.