The application of the Jiles–Atherton (J–A) hysteresis model for numerical modeling of measured quasistatic hysteresis loops of non-oriented soft magnetic material is investigated. The J–A model used assumes its parameters are dependent on actual effective magnetic field strength. This is carried out by using a new parameter associated with the mathematical description of the J–A model. In this paper, the author demonstrates that these varying parameters and the proposed algorithm of parameter estimation are useful in accurate numerical modeling of the static hysteresis loop. Results of modeling are compared with experimental measurements, demonstrating very good agreement in a wide range of maximum field strength. Copyright © 2013 John Wiley & Sons, Ltd.