A magnetic damper composed of a permanent magnet and a conducing plate has the advantage that the magnetic damper can generate a damping force with no physically contact. The conducting plate needs to be thickened in order to obtain a stronger magnetic damping force, since the magnitude of the magnetic flux produced by a permanent magnet is limited. However, it is known that the magnitude of the magnetic damping force is limited, even if the conducting plate of the magnetic damper has a large thickness. It has been considered that skin effect by eddy currents is the cause of this limited magnetic damping force. In addition, it is known that eddy currents have a very slight effect on the natural frequency of a structure with a magnetic damper. In this paper, the coil method considering inductances is proposed as one of the modeling methods for magnetic dampers consisting of a ring magnet and a conducting disk moving relatively in an axial direction. Applying this method, a modal analysis of the free and the forced vibration of a 1-DOF system with a magnetic damper are performed, and the magnetic damping and the magnetic stiffness considering the skin effect, are introduced. Furthermore, the experiments are performed in order to confirm the practicality of the method. The analytical results are found to be in agreement with the experimental results.