This paper proposes a method to derive the frequency response of an actuator with a solid iron core. This actuator is designed for a thrust magnet bearing of a high-speed motor. The actuator is treated as a distributed system with eddy currents in the solid iron core. Theoretical formulation of the frequency response is derived by using Maxwell's equations and by using a simple magnetic circuit model. The finite element analysis results and the experimental results are also obtained. A method for obtaining the rational expression of the frequency response is derived. Although the method is essentially based on a least-square method, it is modified to some extent in order to obtain a rational expression. By using this rational expression, we show that the controller for the magnetic bearings can be designed with usable accuracy, before manufacturing the actual actuator.