Device for storing an automotive vehicle transversely relative to its longitudinal axis on a parking space of a storage facility, having a surface-manoeuvrable, driverless vehicle transporter which is disposed parallel to the longitudinal axis of the automotive vehicle when receiving the automotive vehicle and has horizontally extending pairs of forks which are disposed thereon at one side and perpendicularly, the forks of the pairs of forks being displaceable individually horizontally along the vehicle transporter and the pairs of forks moving under wheels respectively of a vehicle axle from one side of the automotive vehicle in order to grip the wheels by displacing the individual forks horizontally towards each other, whereupon the automotive vehicle is lifted for transporting, surface-manoeuvrable supports (4) being disposed on the vehicle transporter (1) respectively at the end-side, which supports extend horizontally and parallel to the pairs of forks (3) and, when the pairs of forks (3) move under the wheels (8), move past the automotive vehicle (7) at the front- and rear-side at a small spacing, the spacing between the supports (4) being adjustable, a measuring device (6), before the automotive vehicle (7) is received, determining its length, axle positions and the position of the automotive vehicle (7) in space, the surface-manoeuvrable, driverless transporting means (1) adapting, with the data transmitted from the measuring device (6), its length determined by the spacing of the supports (4) and the position of the pairs of forks (3) automatically to the dimensions of the automotive vehicle (7) to be received, and the load absorbed upon lifting the automotive vehicle (7) being transmitted, on the one hand, by the vehicle transporter (1) and, on the other hand, by the surface-manoeuvrable supports (4) to the travel surface.