This paper presents the modeling of synchronous machines under eccentric rotors. The winding function theory accounting for all space harmonics and presented by earlier researchers has been modified to adopt non-symmetric air-gap for the calculation of machine winding inductances. The effect of dynamic air-gap eccentricity on the inductances of a salient-pole synchronous machine using the modified winding function approach (MWFA) has been discussed. Coupled magnetic circuits approach has been used for simulating the machine behavior under healthy and eccentric rotor conditions. The simulation results are in close agreement with the experimental results.