In this paper, an analytical method for the computation of the electromagnetic field in the airgap of an inset permanent magnet synchronous machine is proposed. The originality lies in the fact that both the stator and rotor saliencies have been taken into account in the analytical procedure. The purpose in to compute both quickly and accurately the magnetic fluxes and instantaneous torque of the machine, in order to minimize torque ripples in an optimal pre-design process. It is shown that the instantaneous torque is in good agreement with finite element results, for a shorter computation time. The model presented here can be used when the 2D approximation of the machine is valid, which is the case for most of machines' topologies.