In this paper, we use a detailed magnetic equivalent circuit (MEC) to improve the analysis accuracy in modeling of electrical machines. We do this for those areas in which the flux routes and consequently the so-called flux tubes are not easily definable (e.g., the air gap or saturated parts). In deriving the MEC, we represent these parts by a detailed reluctance network. Moreover, for those parts in which the saturation usually happens, we implement a nonlinear model. The resultant network is complex and contains a large number of nodes. In order to reduce the processing time, we use a novel reduced order model to simplify the network. This reduced model makes the analysis process faster without missing the accuracy of information in the predefined parts of the machine. Finally, we apply the methods to an axial-flux permanent-magnet motor. The experimental results verify the compatibility between the simulation and laboratory results.