To establish a new model of polishing machine for friable hollow capsule (invention patent ZL201510335040.6), and develop a prototype for the precise polishing of hollow Be capsules. The restriction hole design was used to solve the problem of low stress clamping of sphere. Different numbers of counterweight spheres were added to adjust the sliding friction force and prevent the spheres from flying out of the restriction hole. The upper and lower grinding pans were placed eccentrically to achieve random movement of the spheres. The surface roughness of the polished Be capsules was analyzed by white light interferometer. The model calculation shows that the unpolished spheres always roll periodically in the mode of variable speed and variable acceleration. The periodicity is determined by the rotation frequency of the top pan. The spheres of variable acceleration motion increase the sliding friction components and are beneficial to improving the polishing efficiency. In addition, the surface polishing trajectory presents random walk, which can ensure the polishing uniformity. The fragile beryllium (Be) capsule with a diameter of 1.2 mm and a root mean square surface roughness of 510 nm can be polished to 85 nm in 24 hours by this polishing machine. The rationality and feasibility of the fragile sphere polishing machine model are verified by both theory and experiment. The polishing uniformity and polishing efficiency of fragile spheres are closely related to the placement mode of upper and lower grinding pans, the size of restriction hole and the number of counterweight spheres.