To provide a support mechanism for a longitudinal member of eyeglasses in a barrel polishing machine by which the longitudinal member of eyeglasses such as a temple and a brow bar can be held in the most desirable and nearly constant stationary posture for preventing the longitudinal member of eyeglasses from being excessively polished locally in a polishing barrel for polishing.

A clamping part 23 capable of clamping the longitudinal member P of eyeglasses as a polishing target is formed between a center member 21 and a side member 22 in each workpiece mounting frame 2 by joining the center member 21 and the side member 22 arranged to both ends of the center member 21 by a fixing tool 3. While, elastic retaining pieces 4, 4 are respectively arranged to both side edge parts of the center member 21 and the facing edge parts of the side member 22. A large number of guide grooves 41, 41 are formed to the elastic retaining pieces 4 in the vertical direction. Each longitudinal member P of eyeglasses as the polishing target is set by being clamped with each clamping part 23 formed by the contact of the center member 21 with the side member 22 in the workpiece mounting frame 2.