Vibration isolation of a rigid body on compliant mounts has many engineering applications. An analysis for solving these problems using a rigid body simulation and a penalty function optimization is discussed. The simulation is used to calculate natural frequencies and mode shapes, which are a function of the mount design parameters. Laboratory testing results are presented which verify the accuracy of the simulation. The optimization procedure penalizes natural frequencies in an undesirable frequency range and also large design changes. This penalty function is minimized by changing the mount design paramters consisting of the location, stiffness, and/or orientation. The result is a set of design parameters defining a vibration isolation system with natural frequencies moved away from the center of the undesirable frequency range. An interactive computer program was written which allows the engineer to use this technique as a design tool.