Materials that develop large strokes under precise and rapid control exhibit a great potential in mechanical engineering. Actuators made from those kinds of materials could replace hydraulic, pneumatic, and electromagnetic drives in many applications. However, no such materials are available to date. Piezoelectric and magnetostrictive materials exhibit rapid response, but their strokes are small. In shape memory alloys, strokes are large, but their control is slow due to thermomechanical control. Magnetic control of the shape memory effect was recently suggested by the present author for a principle of new kinds of actuator materials. These materials can develop strains of several percent, and their control is rapid and precise. Actuation of these materials is based on the reorienting of the twin structure of martensite or the motion of austenite-martensite interfaces by applied magnetic field. In the present report, magnetically induced motion of the austenite-martensite interfaces is demonstrated in an Fe-33.5Ni alloy.