Abstract: A necking apparatus for producing a smooth, inwardly tapered necked-in portion on a cylindrical container includes a plurality of necking modules and a turret which is rotatably mounted in each module about an axis of rotation. Each turret includes an upper turret frame which is mounted on the axis of rotation and which can be moved axially relative to the turret and a lower turret frame. A plurality of necking dies are mounted on the upper turret frame, and a plurality of container supports are axially aligned with the necking dies and are mounted on the lower turret frame for axial movement. Each necking die includes a necking portion for engaging and necking a side wall of a container as the aligned container support moves a container toward the necking die. The positions of the necking dies are adjusted by spacers so that the necking portion of each die does not engage the tapered necked-in portion of the container as the container support is moved toward the die.