A fall restraint system includes a cable for attachment to a fall restraint harness assembly of a worker. The cable can be attached to a boom arm cantilevered on a mast carried from the ground or can be stretched between two points on opposed walls. A shock absorber is provided for absorbing at least part of the shock forces so as to reduce the loading applied to the support system. This comprises an elongate member with a movable member or sleeve mounted on it for longitudinal movement. The movement is resisted by a friction brake or a compressible material contained within a tube so that the sleeve moves along the tube in response to loads exceeding the normal load to reduce the loading on the cable while compressing the material in the tube.