This paper presents a parametric study and an optimal design of the ER-SFD supporting a rigid rotor system. An attempt is made to obtain the optimal design of an ER-SFD for a two degree-of-freedom rotor model. Such a simple model is used in order to get a better insight into the physics of the problem. A maximum whirl amplitude, supply pressure and voltage are considered, and a maximum whirl amplitude is minimized over a range of speeds and presented f3r some values of unbalance mass. The results presented in this paper provide important design information necessary to reduce a whirl amplitude of an ER-SFD.