A vibration power minimization model is developed, based on the mobility matrix method, for a vibration isolation system consisting of a vibrating source placed on an elastic support structure through multiple resilient mounts. This model is applied to investigate the design optimization of an X-Y motion stage-based vibration isolation system used in semiconductor wire-bonding equipment. By varying the stiffness coefficients of the resilient mounts while constraining the dynamic displacement amplitudes of the X-Y motion stage, the total power flow from the X-Y motion stage (the vibrating source) to the equipment table (the elastic support structure) is minimized at each frequency interval in the concerned frequency range for different stiffnesses of the equipment table. The results show that when the equipment table is relatively flexible, the optimal design based on the proposed vibration power inimization model gives significantly little power flow than that obtained using a conventional vibration force minimization model at some critical frequencies. When the equipment table is rigid enough, both models provide almost the same predictions on the total power flow.