With a wave gear device, the gears employ homothetic curve tooth profiles AD, BE. Furthermore, a transposition is applied to the external teeth along the tooth trace such that the movement loci M.sub.2, M.sub.3 of the external teeth in a section perpendicular to the axis, from the aperture end to the inner end, share the movement locus M.sub.1 of the aperture end and bottom portion thereof, and a continuous meshing of the teeth in the tooth trace direction is achieved. Furthermore, the tooth bottom rim thickness of the aperture end of the external teeth is optimized using a modified Goodman diagram, and a tooth bottom rim thickness which takes into account the relationship between the tooth profile and the transmitted torque from the aperture end to the inner end is employed for the flexible external gear.