A device (1, 1') for automatically unstacking nested, lying containers (6, 6') and setting them on a support, for example a conveyor (3a), with the container opening (6b) facing upwards, has a gripper (5) for holding and moving the first container (6) out of a lying container stack (2, 2'), the gripper (5) being arranged in holders (8a, 8b) movable in the direction of the stack, and a clamping device (4) for retaining the container stack (2, 2') while releasing the front container (6). The gripper (5) is fitted with lateral pressure cylinders (5a; 46) that have horizontal axes located on the same level and are linked to the holders (8a, 8b) which extend above them.