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The principal causes of coercivity in soft magnetic materials are the imperfections in the structure of the crystal, such as inclusion and grain boundaries, that pin domain walls. The models that have been proposed so far in order to explain this effect are only valid for a specific range of material parameters. In this paper, we present a two-dimensional micromagnetic model for Barkhausen coercivity due to inclusions that is valid for all physically realizable material parameters. The details of the interaction between Bloch walls and nonmagnetic inclusions are presented for some interesting special cases. One of the results the model predicts is that walls are stable when they are centered on the inclusion. Furthermore, much higher values of the coercivity are obtained than those predicted by previous models. © 1998 American Institute of Physics.