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This paper discusses the use of the inverted ( -based) Preisach model and its incorporation into the finite-element method (FEM). First, the -based Preisach model is studied thoroughly along with the forward ( -based) Preisach model, highlighting the advantages and disadvantages of both models. The study confirms that, in addition to the main purpose of the -based model—to compute the magnetic field directly—the -based model can overcome the congruency problem. Thus, the -based model proves to be more accurate than the -based model. Second, the paper suggests that incorporating the -based Preisach model into FEM models results in relatively accurate, computationally efficient simulations. The method has been validated by simulating hysteresis torque in a high-speed induction motor, and a comparative investigation of the effectiveness, accuracy, and efficiency of the models has been conducted.