Suspensions are often found in nature and in technological processes. Suspension particles can differ in density and compressibility from the parent medium and affect the speed and attenuation of sound. It is thought that particle suspensions with neutral buoyancy, i.e., the average density and compressibility of which do not differ from the parameters of the surrounding fluid, do not affect sound propagation. However, if a particle’s center of mass is displaced, i.e., it does not coincide with the point of the Archimedes force, in an acoustic field, such a particle executes rotational oscillations. Rotational oscillations are accompanied by viscous friction and lead to loss of acoustic wave energy. A particle’s center of mass can be displaced by a nonuniform density distribution of a body or a point uneven mass on its surface, which in the general case can be both positive and negative (a cavity). The article analyzes sound propagation in suspensions of rod- and disk-shaped particles characteristic of many media. The formulas describing acoustic wave energy losses in a particle suspension are obtained, and the magnitude of additional sound wave attenuation is estimated, which show that this mechanism can lead to appreciable attenuation.