A method is given for obtaining a phase terminal equivalent circuit, which is useful for the analysis of cylindrical induction heating systems for electric energy conversion into heat. The excitation is circumferential and can be realized as either a three-phase system or a single-phase system. The iterative form of the solution allows for solid and hollow charges. First, a general form of the field solution is obtained using transfer matrices. A variable transformation is then made, which makes it possible to derive an equivalent circuit for each annular region in the system. By joining the equivalent circuits in cascade, an equivalent circuit for the complete system is obtained. The voltages and currents in the equivalent circuit relate directly to the field quantities within the actual system.