A process and apparatus for simultaneously securing opposite parallel edge flaps of a flexible cover sheet to opposite parallel edge faces of a wall panel. A pair of wiping devices move downwardly and wipe the edge flap against the edge faces and transversely tension the cover sheet. Top sweep devices move down into holding contact with the cover sheet adjacent the parallel edge faces to maintain the transverse tension in the sheet. The edge flaps are then deflected and adhesive applied to the edge faces and back surfaces of the edge flaps. The wiping devices then again wipe the flaps downward into pressed contact with the edge faces to create an adhesive securement therewith.