In a wave gear device, an annular rigid externally toothed gear is disposed on the inner side of a cup-shaped flexible internally toothed gear. An internal-tooth-formation portion of the flexible internally toothed gear and a pushed portion pushed by a wave generator and flexed ellipsoidally are formed in different positions along the center axis line. The wave generator is disposed on the inner side of the flexible internally toothed gear, the pushed cylindrical portion is pushed from the inner side to the outside along the radial direction thereof by the wave generator, whereby the pushed cylindrical portion is flexed ellipsodially. As the outside diameter dimension of the wave gear device is determined by that of the flexible internally toothed gear, a wave gear device having a small outside diameter dimension can be obtained.