In addition, where a cup-shaped flexible external gear is reduced in its axial length for the purpose of volume reduction thereof, a degree of coning of the flexible external gear becomes larger, and so the defects caused by using the tooth profiles of the above inventions become remarkable.In terms of these defects, there has been a demand for an improvement of the tooth profiles. Inventions disclosed in Japanese Patent Laid Open Nos. SHO 62-75153 and HEI 2-62461 are directed to an improvement for avoiding the above defects. In these methods, however, it is required to apply special additional-processing such as crowing, relieving and the like on teeth. Moreover, no consideration is made in the above publications on the reduction in axial length of a cup-shaped flexible external gear. An object of the present invention is to provide a flexing contact type gear drive which, without requiring special additional-processing such as crowing, relieving and the like, is capable of realizing a wider range of meshing of the teeth along the whole tooth trace direction of a cup-shaped external gear without interference, and at the same time which is easily machined and is capable of reducing an axial length of the cup-shaped flexible external gear.