Modern permanent magnet synchronous machines (PMSMs) may also be operated in regimes where significant magnetic saturation occurs. Classical fundamental wave models do not incorporate magnetic saturation in a systematic way. Mostly, only heuristic extensions can be found in the literature. Control schemes based on such dq0-models are thus often unable to achieve the given control demands. This paper proposes a flatness-based torque control strategy for a saturated surface-mounted PMSM. Different to existing works, magnetic saturation is considered in a thorough and physically consistent way. Based on a calibrated magnetic equivalent circuit model of the PMSM, a simplified model suitable for the flatness-based controller design is derived. The proposed 2-DOF control scheme inherently accounts for the mutual coupling of the phase windings. Furthermore, the time-varying controller gains are obtained by pole placement technique. In contrast to the majority of controllers used for PMSM control, the proposed control scheme is formulated in the stator-fixed reference frame, and hence, no coordinate transformation is necessary. The flatness-based torque controller is implemented on an experimental test bench. An accelerated run-up of the PMSM with about four times the rated torque is performed to highlight the feasibility of the proposed approach. Finally, the flatness-based torque controller is compared with a common vector control implementation based on a dq0-model of the motor.