A tensioning apparatus for tensioning a screen in a vibrating screen separator of the type having a box structure defined by two opposing spaced-apart upright side walls separated by at least one screen bed support structure. Included is an actuator support mounted to an exterior surface of a side wall of a box structure for pivotally securing the stationary end of an actuator thereto. The actuator includes a movable end that is cyclically movable from a first releasing position adjacent the sidewall, to a second engaging position, transversely spaced apart from the side wall, responsive to a track follower moving along a track inclined transversely to the side wall of the box. A clamp rail assembly is fixed to the movable end of the actuator to engage and tension a screen responsive to transverse movement of the movable end of the actuator.