System for mounting screen and other panels in vibrating and other screening apparatus in which longitudinal channel members interposed between laterally adjoining panels and anchored to apertured longitudinal supports, have spaced normally upright flexible sides each yieldably flexing inwardly in response to pressing of a panel edge thereagainst for seating the edge in an external groove in the channel side, the channel member containing a longitudinally coterminous cavity opening upwardly through a relatively restricted slot, and the panel edge being releasably lockable in the channel groove by a T-shaped lock member having a stem insertible in said cavity through said slot for forcing the flexed side to return to upright edge-locking position. The system also includes clamps on sides of the apparatus for clamping contiguous outer sdges of screen panels thereto, reinforcing of profile wire screens by socketing projected ends of their tie rods in molded screen edges, and for vibrating screening apparatus, dams mounted at predetermined longitudinal intervals for retarding flow through the apparatus.