The quantitative analysis of the iron loss taking magnetic hysteresis behavior into account is essential for the development of high-efficiency electric machines. In a previous paper, a novel magnetic circuit model incorporating a play model, which is one of the phenomenological models of magnetic hysteresis, was proposed. It was clear that the proposed model can calculate the hysteresis loop of a ring core with high speed and high accuracy. However, this method was applied only for the objects with simple shapes. Thus, it is necessary to extend the applicable range for the objects with more complicated shapes. This paper presents a novel reluctance network analysis (RNA) model incorporating the play model and indicates the validity of the proposed RNA model by using a three-phase-laminated-core variable inductor as an object of discussion.