In order to simulate the electrical states such as currents of stator and rotor windings accurately in fault conditions， and to find out the physical principles behind inter-turn short circuits of field windings in non-salient pole synchronous machines， it is necessary to calculate the parameters of the machine accurately， especially the inductances of the filed windings with inter-turn faults. Given that non-salient pole synchronous machines feature distributed field windings， this paper calculates the inductances of single field coils using the harmonics analysis method and air-gap permeance concept， and derives the multi-loop parameter model based on the actual connection of the field winding with inter-turn faults. The parameter model considers the harmonics of magnetic-field caused by the fault loop in field winding， and is justified by several inductance calculation examples in this paper. Substituting the parameter model into the multi-loop model for inter-turn short circuit faults of field winding， the currents of all the stator and rotor loops in non-salient pole synchronous machines are derived. The results coincide well with the experiment results on a model machine. The correctness and accuracy of the parameter model are thus verified.