The reduction of noise emissions is a central target in positive displacement pump design, and the mitigation of structure borne noise is a main approach toward that goal. Particle damping offers a passive means of vibration mitigation without input energy requirement nor compromising the pump function and efficiency. The principle was applied to an axial piston pump and tested in sound power and structure borne noise measurements. A hollow encasing, which envelops most of the pump's sound emitting surface, is mounted, simultaneously providing particle damping and vibration decoupling properties. Finally, damping cavities are introduced modifying the pump's swash plate and end casing. Design considerations and experimental performance of the particle dampers with regards to sound power, sound quality, structure borne noise, and modal behaviour are presented and discussed. The mounted particle damped encasing provides a marked reduction of emitted sound power and improved sound quality. Meanwhile, no systematic acoustic improvement was observed for the particle dampers in the swash plate and end casing, which may be attributable to the pump's modal behaviour.