An apparatus and process for causing excess covering material at a workpiece corner to be gathered, folded and secured to a back side of the panel. A corner tucking apparatus includes a gathering plate positioned adjacent a positioning structure, and moves inwardly across the back side of the workpiece, from the corner, to gather and fold the corner flap. The gathering plate has a generally V-shaped notch which causes excess material to be gathered together as the plate moves inwardly. The gathered material upon reaching the apex of the notch is folded downwardly into contact with the back side of the workpiece. A securing structure which is carried inwardly with the gathering plate is then activated to fixedly secure the folded flap to the pad or workpiece.