A compact directional acoustic sensor is described which uses a two-fiber optical probe, a light emitting diode (LED), a photo-diode detector, and a slender cylindrical cantilever to the end of which is attached an optical reflector. Acoustically induced transverse displacement of the cantilever tip modulates the light reflected by it into the collection fiber, which conveys the light to a photo-detector. Directional sensitivity is achieved through the dependence of the collected light on the cosine of the angle between a line through the centers of the two fibers and the cantilever tip displacement (the sound direction). The sensor requires relatively low power, and its LED source has low levels of 1/f noise. These attributes make it a good choice for remote low frequency applications requiring long operating lifetimes. An analytic model of the acoustic response of the cantilever is constructed, which is partially verified using a finite element model and experimentally validated using measurements of the acoustic response in air. The model is used to predict to what extent and over what frequency band that response depends upon the acoustically generated flow (drag) force [Yuan et al., IEEE Sensor J. 8, 1114-1117 (2008)].