According to the present invention, a flexing contact type gear drive having a cup-shaped flexible external gear can be realized which makes it possible to form a smooth meshing of teeth all over to the end portion of tooth trace of the diaphragm without additional processings such as crowning and relieving to the external gear, and thus, with maintaining the tooth thickness constant. While, simultaneously it is possible to provide a flexing contact type gear drive of high strength, rigidity and precision and of small size