Abstract: A cover for containers and especially of the plastic snap-on type for drinking cups and the like is provided with a downwardly outwardly extending peripheral skirt. The skirt is in turn provided with a plurality of circumferentially spaced radially outwardly directed flutes as well as a plurality of alternatively adjacent inwardly directed detent portions or lands in part defined by the aforementioned flutes. Upper inner surface portions of the lands are adapted to engage the outer peripheral bead of the container which the cover is adapted to close while construction of the flutes simultaneously provides for a degree of limited circumferential expansion so as to accommodate the manufacturing dimensional tolerances in the container bead. The flute construction also enables major portions of the skirt to be upwardly outwardly flexed to further accommodate such dimensional variations.