The invention concerns a device for bending glass sheets comprising an upper bending shape and a bending support, said upper bending shape and/or said bending support being laterally movable relativeto each other, said bending support comprising a blank mould for bending a glass sheet by gravity and a pressing mould configured to press the glass sheet against said upper shape, one of said two moulds of the bending support being surrounded by the other, when viewed from above, at least one of said two moulds of the bending support being movable in a vertical direction relative to the other. The invention further relates to a bending method using said device.