in this paper, the winding function theory (WFT) is modified and used to calculate the inductances of a synchronous machine which has strongly non uniform air gap. For the first time, a numerical air-gap function is used in addition to a model of the air-gap of salient-pole machines which considers the stator slot effects. the modified winding function(MWF) method introduced here is more precise when compared with pervious methods. this MWF enables one to compute the air-gap function more accurately.