It is demonstrated that hysteresis in the magnetostriction k is coupled to hysteresis in the magnetization M because of the dependence of the magnetostriction on the magnetization. At the same time, when stress is present, the magnetization is in turn coupled to the behavior of the part of the magnetostriction associated with domain moment rotation. An expression for the magnetostriction is formulated, and numerical modeling results for magnetostriction hysteresis are compared to experimental results. Although some features of the magnetostriction in iron and steel still need additional explanation, the main features of the magnetostriction are accounted for. These include liftoff (failure of the magnetostriction to return to its value in the demagnetized state as the hysteresis loop is cycled) and a magnetostriction increase after flux density B reaches its maximum and starts to decrease. A macromagnetic, multidomain formulation that yields zero magnetostriction in the demagnetized specimen is used. >