This paper presents a method for the computation of the incremental inductances in a 12/10 variable flux reluctance machine using the hybrid analytical modeling coupled with a fixed-point nonlinear solver. The variation of incremental and apparent inductance with respect to the dc-field excitation is investigated for both zero and non-zero ac-field excitations. The results show that the difference between both inductance values is not negligible after 25 A/mm2 dc-current density for the investigated benchmark without the ac field. Moreover, when a non-zero ac field is introduced in addition to the dc-field, the apparent inductance becomes misleading not only under magnetic saturation but also under low excitation in the linear region of the saturation curve. The results obtained with the proposed nonlinear hybrid model are compared with the finite element method in terms of magnetic flux density distribution and incremental inductance value. The root-mean-square discrepancy of magnetic flux density distribution is found to be 37.6 mT. Furthermore, the discrepancy between incremental inductance results of the proposed method and the finite element model is calculated as 1.43%, while the proposed approach requires less post-processing and necessitates ten times less number of degrees-of-freedom.