The flexible external gear of a strain wave gearing is provided with: a cylindrical body part capable of flexing in the radial direction; external teeth formed on the outer circumferential surface thereof with a constant pitch; and grooves formed on the inner circumferential surface of the cylindrical body section along the circumferential direction thereof with the same pitch as the external teeth. The grooves are grooves with a wave-shaped cross-sectional shape having the center line of the tooth crest of the external tooth as the center and extend in the width direction of the external teeth. It is possible to increase the tooth bottom fatigue strength of the flexible external gear by increasing the tooth bottom thickness, while maintaining ease of flexing and a tooth shape that can withstand tangential forces due to meshing.