An apparatus for the making of container jackets from flat cardboard or plastic blanks. The blank is folded around a core by means of pivoted fingers which are moved toward the core while ends of the fingers are guided in guide passages to produce pivoting of the fingers. The fingers pivot such that blank-engaging ends of the fingers fold the blank around the core. The slide guides are mounted for pivotable movement simultaneously with the movement of the fingers toward the core, whereby the movement of the fingers can be adapted to cores of different diameter by changing the distance of movement of the carrier, i.e., the same fingers and slide guides can be used with an infinite number of core diameters.