To provide a supporting structure or the like for a rear sub-frame enhancing yaw responsiveness at an initial stage of turning and enhancing stability at regular turning.

The supporting structure for the rear sub-frame 10 is attached to a vehicle body through a front side elastic body mount 20 and a rear side elastic body mount 30 arranged so as to be spaced in a longitudinal direction of the vehicle, and a suspension arm of a rear wheel suspension device is connected. The rear side elastic body mount 30 has non-linear characteristic that spring constant relative to lateral force SF inputted from the suspension arm to the rear sub-frame 10 is increased according to increase of the lateral force. A displacement amount caused by the lateral force is larger than the front side elastic body mount at the initial area where the lateral force is small, and the displacement amount becomes smaller than the front side elastic body mount at the regular turning area where the lateral force is larger than the initial area.