The wave generator of a strain wave gearing is provided with an ellipsoidally contoured wave generator plug and a wave generator bearing. The wave generator bearing is provided with an annular body fitted between inner and outer races in a sliding contact state. The annular body is composed of an endless coil spring and has a rigidity that is able to maintain a constant gap between the inner and outer races. The annular body also has a specified overall flexibility in the radial direction so that the annular body can be flexed into an ellipsoidal shape by the wave generator plug. Since sliding occurs between the annular body and the inner race when the wave generator plug rotates, it is possible to generate a wave motion in an externally toothed gear with a small rotational torque.