A suspension method for stabilizing a bicycle frame is provided with an elastically deformable damping suspension in order to absorb shocks, wherein said method consists of elastically deforming a suspension device by a torsional effect perpendicularly to the bicycle frame. The suspension device extends over a frame plane and is fitted out to implement the method by providing a damping torsional device arranged about at least one axis contained in a torsional plane perpendicular to the frame plane.