An externally toothed gear of a strain wave gearing is made to flex into a shape conforming to an ellipsoidal curve. The externally toothed gear meshes with an internally toothed gear at the major-diameter position of the ellipsoidal curve. These two meshing positions gradually change in the circumferential direction of the both gears along the tooth trace direction. The number of external teeth of the externally toothed gear participating in meshing with the internally toothed gear can be increased. A strain wave gearing which has a high rigidity and is capable of reducing vibrational noise, can be realized.