A waste storage device includes a container in which a cassette is mounted. Tubing is pulled through the centre of the cassette to store packages separated by twists. The cassette is rotated relative to the container to provide the twists between packages by virtue of a rotatable disk and user grip portion. The package is gripped against rotation by a gripper diaphragm and is guided towards a wall of the container by a guide diaphragm to prevent untwisting between packages.