The process, applicable to sealed packages (11) containing foodstuff provided with two end flaps (12) disposed in substantially coplanar relation with the packages themselves and extending outwardly from the opposite sides of the same, carries out the bending of said end flaps (12) at right angles to their extension direction, the folding back of te corners (12a) of said flaps, a further folding over of het end flaps (12) themselves as far as they are disposed upon the packages, in contact therewith, and the subsequent application of an enfolding band made of covering material in order to form a wrapping retaining said end flaps (12) after their folding back.