Eddy currents are evident in solid-core active magnetic bearings (AMBs), but they are omitted in the commonly-used models, leading to a significant error between the analytical model and the real system. Based on the magnetic circuit method, this paper presents an analytical model including the eddy-current effects of a solid-core AMB under both current drive and voltage drive, after setting up the relationship between the magnetic force and the effective reluctance. A half-order term is induced in the effective reluctance due to eddy currents, turning the analytical model to fractional-order. The effective reluctance only appears in the coefficient of the s2-term, and affects the system dynamics under current and voltage drives distinctively. The half-order term changes the order of the model from 2 to 2.5 under current drive, whereas the order of the model is not changed and is still kept 3 under voltage drive. System identification of a solid-core AMB verifies the proposed models, which indicates that the voltage drive can effectively reduce the eddy-current effects compared with the current drive. In addition, although the solid-core AMB shows fractional-order characteristics, it can be described well with an integer order model under voltage drive. As a result, the voltage drive is a more reasonable choice to a solid-core AMB, since it avoids the complex fractional-order modeling and control.