The system has the garage modules stacked over each other as well as side by side. The cars are moved to the selected modules by a lifting platform (5) supported at the corner by four upright supports (3). These are secured in foundations for a simple vertical stack or move along guide rails (15) for a lateral stack of modules. The lifting platform has a grid structure deck and is fitted with side railings (9). The hoist system includes a safety barrier (10) at ground level (11) as well as pivot mounted panels (7) which bridge the gap between the platform and each module. The system can be operated by remote control from the vehicle.