A plurality of tubes (12, 13, 14) are arranged vertically in a closed row along a circle within a completely enclosed housing (1) provided with an inner radiation protection jacket (4). All the tubes (12, 13, 14) are connected as an assembled unit to a vertical shaft (17) which is mounted for rotation between a top plate (2) and a bottom plate (3) of the housing (1). A waste bag (18) can be inserted through an opening (8) in the top plate (2) into the tube (12) located at the time below same, into which bag radioactive waste (19) can be introduced also through the opening (8) which can be closed by a lid (9). Another opening (20) is provided in the bottom plate (3), it being located below the last tube (14) of the row in the intended direction of rotation of the unit. Thus, the bag (18) which is present in the corresponding tube (14) drops through said further opening (20) into a reception container (7) placed below it. When the unit is turned further daily by an amount equal to the angle between two adjacent tubes, sufficient time automatically elapses to permit the radioactivity of the waste in the filled bags which are no longer accessible to drop to an unobjectionable value until the bags fall into the reception container (7) and can be safely eliminated from there.