The well‐known Barkhausen effect occurs when a domain wall moving through a crystal gets ’’hung up’’ at imperfections. A numerical model is described here that gives a possible mechanism for this effect. It is assumed that the imperfection is a spherical nonmagnetic inclusion in an otherwise perfect ferromagnetic material. The equilibrium wall shapes, as the applied field is slowly increased, are successively computed. When the wall ’’touches’’ the hole, the induced pole strength decreases and a sudden irreversible change is triggered. The field strength at which this takes place is the coercive force. A new numerical techique is introduced to overcome the ’’stiff’’ equations encountered. A discussion of these techniques will be included in this presentation.    a) Work supported by National Science Foundation grant.