A ledge for resiliently supporting a paper making machine wire has a head ledge which extends across the direction of travel of the wire and over which the wire can slide. The head ledge is rigidly connected to a movable support ledge which also extends across the direction of travel of the wire and is guided on a stationary support structure. Between the movable support ledge and the stationary structure there is a resilient push device which can displace the movable support ledge together with the head ledge between a position of rest away from the wire and an operating position in which the head ledge is pressed with a predetermined force against the wire. The stationary structure has several guide arms distributed over the length of the support ledge which are the exclusive means for guiding the movable support ledge. Several guide arms arranged in pairs are provided which grip around the support ledge, in the manner of a clamp.