A support device (1) for supporting motor vehicles, with two plate-like bodies, wherein one of these plate-like bodies is a base plate (2) and the other of these plate-like bodies is a support plate (4) capable of being laid on this base plate (2), wherein the base plate (2) has a first even surface (2a) which is opposite a second even surface (4a) of the support plate (4) and wherein the support plate (4) has a support face (4b) for supporting the motor vehicle. According to the invention the support device (1) has a separation device (6, 62, 32, 34) which at least for a time generates a force which acts between the base plate (2) and the support plate (4) and which holds the support plate (4) in a hovering state above the base plate (2), in which hovering state, in particular, the first even surface (2a) and the second even surface (4a) do not touch each other.