Single crystal Ni-Mn-Ga ferromagnetic shape memory alloys (FSMAs) are active materials that produce strain when a magnetic field is applied. The large saturation strain (6%) of Ni-Mn-Ga and material energy density comparable to piezoelectric ceramics make tetragonal Ni-Mn-Ga an interesting active material. However, the usefulness of the material is limited by the need for electromagnets to produce a magnetic actuation field. In this paper, an actuation method for shape memory alloys in the martensitic phase is described, in which asymmetric acoustic pulses are used to drive twin boundary motion. Experimental actuators were developed using a combination of Ni-Mn-Ga FSMA single crystals and a piezoelectric stack actuator. In bidirectional actuation without load, strains of over 3% were achieved using repeated pulses (at 100 Hz) over a 30 s interval, while 1% strain was achieved in under 1 s. The maximum strains achieved are comparable to the strains achieved using bidirectional magnetic actuation, although the time required for actuation is longer. No-load actuation also showed a nearly linear relationship between the magnitude of the asymmetric stress pulse and the strain achieved during actuation, and a positive correlation between pulse repetition rate and output strain rate, up to a pulse repetition rate of at least 100 Hz. Acoustic actuation against a spring load showed a maximum output energy density for the actuator of about 1000 J/m3, with a peak-to-peak stress and strain of 100 kPa and 2%, respectively.