Abstract: An apparatus is provided for the individual production of rigid containers that are open on one side, such as cones or cups, by inserting the containers into dimensionally stable individually produced sleeves which are matched to their external contour. The containers are transported through by a transport apparatus having a plurality of transport tracks lying beside one another under a discharge apparatus, which deposits the sleeves in the transport tracks. The discharge apparatus includes a support provided with discharge channels extending obliquely downward for the bar-shaped stacks of sleeves, a holding apparatus disposed downstream of the support, for the stacks of sleeves, and a transfer apparatus having a carriage which is provided with suction heads, can be moved back and forth above the transport tracks and draws the sleeves off the stacks of sleeves with its suction heads and deposits them on the transport tracks.