A mesh-based magnetic equivalent circuit has been derived to model the dynamics of wound rotor synchronous machines (WRSMs). A particular focus has been placed on the derivation of flux tubes to model machines with an arbitrary number of damper bars placed at an arbitrary depth in the rotor pole tip. Faraday's Law is applied to establish a state model in which winding and damper bar flux linkages are selected as state variables. The resulting coupled magnetic equivalent circuit/state model is solved to predict machine dynamics. An important attribute of the model is that saturation is represented without the need for a relaxation factor, which enables its use as a practical tool in machine design. Data obtained from hardware experiment and a finite-element model are used to validate the proposed methods.