A two degree-of-freedom model, consisting of a rigid rotor supported on rigid bearings which are in turn supported on squeeze film dampers, is considered. Isotropic centering springs are assumed resulting in a steady synchronous centered circular response for the rotor. The resulting nonlinear system is modeled in nondimensional form. The transmissibility ratio of the system as well as the power dissipated are minimized for various values of unbalance and at several speeds, with the squeeze film bearing parameter as the primary design variable. Expressions are derived for linear variational stability of the circular orbit, and are imposed as constraints in the optimization process. The dependence of the optimal configuration on speed and unbalance is discussed.