A wave generator for a strain wave gearing makes a flexible externally toothed gear to flex into an elliptical shape and mesh with rigid internally toothed gears, and makes meshing positions of the flexible externally toothed gear with the both gears to move in a circumferential direction. On the inner side of a rigid plug of the wave generator, a plug support ring is secured and integrated. The rigid plug is formed from an iron-based material, and the plug support ring is formed from a high-rigidity material that is more rigid than the iron-based material. Since deformation of the rigid plug is suppressed, the wave generator provided with a large hollow part can be obtained.