Abstract: Apparatus for shock-absorbingly supporting a bicycle seat on a bicycle frame. A longitudinal beam means is pivotably attached via transverse bearings a first end to the frame, the beam bearings being configured to permit pivot motion only in a plane containing the bicycle frame. The beam is supportive of seat device near an opposite end of the beam. Shock absorbing means, preferably an adjustable gas strut, is disposed below the beam, and is connected at a first strut end to the frame and at an opposite strut end to the beam adjacent the seat device to form a triangular strut shock-absorbing suspension for the seat device wherein the triangle side comprising the strut is variable in length. In a preferred embodiment, the length of the strut may be remotely adjusted by the rider to vary the distance between the seat and the pedals or ground. In a further preferred embodiment, the beam includes a control to adjust the attitude of the seat in accordance with the height thereof.