However, the each of the above inventions is directed to a flexing contact type gear drive of the type having a cylindrical flexible external gear called as a flat type or a pan cake type. Therefore, the change in deflection along an axis of the flexible gear caused by coning when the cup-shaped flexible external gear is employed, is not taken into consid eration. Hence, the proposed tooth profiles function properly at a specific section of tooth trace (for example, at a section of non deviation), but at the other sections, defects such as non contact of the teeth, tooth interference and the like may occur. As mentioned above, although the tooth profiles of the above inventions are effective for a case where the cylin drical flexible external gear is employed, they are not applicable for a case where the cup-shaped flexible external gear is employed