The parking system has platforms (10) onto which the cars are parked. The platforms are raised by rams (8,9) to stack one car over another. The rams grip the ends of cross members (12), which are fixed off-centre on the platforms to support the platforms. The cross members have a profiled cross section. The ends of the cross members fit through recesses in side plates that border the platforms. The cross members have slits to locate locking blocks attached to the upper ends of the rams using swivel joints. The locking blocks are secured inside the cross members.
