Storing vehicle tire casings (4) by providing at least two channels (12) for storing casings, each one having an end stop (22), and a casing conveyor, capable of coming into alignment with any of the channels and containing a platform (32) that can receive a casing. A casing located in the channel is lifted until it is higher than the end stop. The lifting is done by a roller (46), which is mounted in such a way that it can move in the vertical direction in relation to the platform.