The motions of a rigid and unconstrained prolate spheroid subjected to plane sound waves are computed using preliminary analytic derivation and numerical approach. The acoustically induced motions are found comprising torsional motion as well as translational motion in the case of acoustic oblique incidence and present great relevance to the sound wavelength, body geometry, and density. The relationship between the motions and acoustic particle velocity is obtained through finite element simulation in terms of sound wavelengths much longer than the overall size of the prolate spheroid. The results are relevant to the design of inertial acoustic particle velocity sensors based on prolate spheroids.