The interior space of a cup-shaped flexible externally toothed gear of a cup-type wave gear device is divided into a front interior space and a rear interior space by a partition mechanism. A lubricant is filled in the front interior space at the side of a wave generator, to which lubrication is required. The volume of the front interior space is set so that a necessary amount of lubricant is filled. Since the lubricant is not necessary to fill in the entire interior space of the flexible externally toothed gear, the amount of lubricant to be filled can be reduced.