Ferromagnetic shape memory alloys have demonstrated strains up to 5% resulting from the rearrangement of crystallographic variants by twin boundary motion under an applied field. A model is proposed that describes twin boundaries moving abruptly in order to accommodate either the mechanical energy of an applied stress σЄ0 or the magnetic interaction energy of the applied field MsH. This model provides predictions of the materials response under both field and load. The principal conclusion of the model is that when one energy, either mechanical or magnetic, becomes larger than the other, the twins will move to abruptly rearrange the entire sample to a variant stable under the new condition. Experiments were performed to verify this model in Ni–Mn–Ga shape memory alloy. The abrupt change of the variant structure was observed experimentally although the twin boundaries only swept through limited potions of the sample. Experimental field-induced strains reached 2.2%. Samples were also tested under cycled field with constant load and showed cyclic strains of 1.5%. © 2001 American Institute of Physics.