A flat strain wave gearing device equipped with: a first internal gear and a second internal gear; a flexible tubular external gear; and an elliptically shaped wave generator. In the direction of a central axis, the center of support of the external teeth by the wave generator is offset, by an offset amount of Δ along the direction of the central axis, with respect to the tooth-width center of the external teeth of the external gear. By setting the offset direction and the offset amount appropriately it is possible to achieve a strain wave gearing device which is suitable in terms of the operating conditions and the mechanical characteristics of the first and second internal gears.