A mechanism for magnetostriction in the highly magnetostrictive material Terfenol-D is explained in detail. This mechanism is based on a theory of magnetostriction [R. D. James and D. Kinderlehrer, Philos. Mag. B 68, 237 (1993)] that is particularly suited to predictions of the macroscopic behavior of materials that exhibit large magnetostriction. Some experiments that test these predictions are proposed.