A strain wave gearing comprising: a rigid internal gear, a flexible external gear arranged coaxially inside of the rigid internal gear, and a wave generator fitted inside the flexible external gear; wherein the external gear is ellipsoidally flexed by the wave generator, and external teeth of the ellipsoidally flexed external gear mesh with internal teeth of the internal gear in regions avoiding sections at either end in a major axis direction of the ellipsoidally flexed external gear; the internal gear, and the external gear prior to ellipsoidal deformation, both are spur gears of module m; a number of teeth of the external gear is fewer by 2n than a number of teeth of the internal gear, where n is a positive integer; at a major axis location on an ellipsoidal rim neutral curve of the external gear in an axis-perpendicular cross-section at a prescribed location lying in a tooth trace direction of the external gear, a radial flexing amount with respect to a rim neutral circle prior to flexion is 2κmn, where κ is a deflection coefficient, and where an axis-perpendicular cross-section established at a prescribed location lying in the tooth trace direction of the external gear is taken as a principal cross-section, the principal cross-section being a non-deflection flexing cross-section in which the deflection coefficient κ = 1; based on a movement locus of κ = 1 by the teeth of the external gear with respect to the internal gear, where meshing of the external 18 174 156.2 gear with respect to the internal gear in the principal cross-section is regarded as rack meshing; a tooth profile of an addendum of the internal gear is specified by the following formula a, x Ca 1 = 0.25 mn π + θ − sin θ y Ca 1 = 0.5 mn − 1 + cos θ where 0 ≤ θ ≤ π; a tooth profile of an addendum of the external gear is specified by the following formula b, x Fa 1 = 0.25 mn π − θ + sin θ − ε cos θ / 2 − sin θ / 2 2 y Fa 1 = mn 0.5 1 − cos θ − ε / 4 sin θ / 2 − cos θ / 2 2 where 0 ≤ ε ≤ 0.1 and 0 ≤ θ ≤ π; and the tooth profiles of the dedenda of each of the internal gear and the external gear are set to any shape that does not interfere with the tooth profile of the addendum of the other gear (2,3). a rigid internal gear, a flexible external gear arranged coaxially inside of the rigid internal gear, and a wave generator fitted inside the flexible external gear; wherein the external gear is ellipsoidally flexed by the wave generator, and external teeth of the ellipsoidally flexed external gear mesh with internal teeth of the internal gear in regions avoiding sections at either end in a major axis direction of the ellipsoidally flexed external gear; the internal gear, and the external gear prior to ellipsoidal deformation, both are spur gears of module m; a number of teeth of the external gear is fewer by 2n than a number of teeth of the internal gear, where n is a positive integer; at a major axis location on an ellipsoidal rim neutral curve of the external gear in an axis-perpendicular cross-section at a prescribed location lying in a tooth trace direction of the external gear, a radial flexing amount with respect to a rim neutral circle prior to flexion is 2κmn, where κ is a deflection coefficient, and where an axis-perpendicular cross-section established at a prescribed location lying in the tooth trace direction of the external gear is taken as a principal cross-section, the principal cross-section being a non-deflection flexing cross-section in which the deflection coefficient κ = 1; based on a movement locus of κ = 1 by the teeth of the external gear with respect to the internal gear, where meshing of the external 18 174 156.2 gear with respect to the internal gear in the principal cross-section is regarded as rack meshing; a tooth profile of an addendum of the internal gear is specified by the following formula a, x Ca 1 = 0.25 mn π + θ − sin θ y Ca 1 = 0.5 mn − 1 + cos θ where 0 ≤ θ ≤ π; a tooth profile of an addendum of the external gear is specified by the following formula b, x Fa 1 = 0.25 mn π − θ + sin θ − ε cos θ / 2 − sin θ / 2 2 y Fa 1 = mn 0.5 1 − cos θ − ε / 4 sin θ / 2 − cos θ / 2 2 where 0 ≤ ε ≤ 0.1 and 0 ≤ θ ≤ π; and the tooth profiles of the dedenda of each of the internal gear and the external gear are set to any shape that does not interfere with the tooth profile of the addendum of the other gear (2,3).