The transmission of harmonic vibratory power from a vibrating rigid body into a thin supporting cylindrical shell through multiple passive and active isolators is investigated theoretically. The model allows for the transmission of vertical and horizontal harmonic forces and moments about all three coordinate axes. Results show that over a frequency range from 0 to 200 Hz, the real power transmission into the supporting shell can be reduced substantially by employing in parallel with existing passive isolators, active isolators adjusted to provide appropriate control force amplitudes and phases.