A design optimization of a variable displacement compressor, in order to minimize its crankshaft vibration, is presented. A vibration mount installed between the flywheel and crankshaft is used as the optimizing element; the stiffness and damping values of the mount are selected so that the shaft vibration level is minimized over the cruise speed range while the maximum twist angle acceleration amplitude and transmitted torque are kept within acceptable limits for the entire operating speed range. An asymptotic analysis is used to obtain the nonlinear vibrational response. This analysis provides analytic expressions for the motion and forces in terms of the operating speed and other geometric, kinetic, and dynamic parameters. Consequently, the calculation of the objective and constraint functions is simple to do. A result of the analysis is that the optimal design is insensitive to changes in the magnitude and shape of the cylinder pressure excitation.