An apparatus for moving containers may include a stacking system for forming several overlapping layers of containers and a feeding line for feeding the containers to the stacking system. The stacking system may include a first pick-up head for picking up a group of the containers from the feeding line to form one of the layers. The first pick-up head may include one or more suction nozzles for sucking the group of containers and lateral compression sides which laterally retain the group of containers.