We propose a mechanical model of the vibration isolation system for a satellite flywheel. First, we derived the variation of the natural frequency of the flywheel isolation system under elastic support, considering both the rotation and the precession of the flywheel. The natural frequency of the isolation system was shown to intersect with the dividing frequency related to the spin rate in the low frequency range, which would deduce low frequency resonance. The experiment verified the frequency variation and the resonance at low frequencies. In order to solve the low frequency resonance problem, the damping of the vibration isolation system was increased, and the positive effect was tested and verified.