In order to achieve the above object, according to the present invention, reference is made to the fact that is originally disclosed by one of the present inventors of the present invention in Japanese Patent Application No. HEI 3-357036. That is, in a flexing contact type gear drive, moving loci of teeth of the cup-shaped flexible external gear at respective sections of rotation along the tooth trace direction thereof are found to be changed and decreased in deflection along the tooth trace direction viewed from the opening side of the flexible external gear, and that these moving loci are found to form a single envelope when these moving loci are overlapped on a same plane and the obtained envelope is similar to a curve obtained by similar transfor mation at a reduction ratio of 1/2 of a moving locus at a section of non deviation of the opening of the external gear. In this patent application, a rack approximation method is introduced to simplify the analysis in finding a formula of the obtained envelope. Moreover, a moving locus of the flexible external gear is obtained at a section of rotation near and outside the diaphragm-side end of the flexible external gear, and is connected to the envelope to thereby form a composite curve