An automatic packing device (1) for cushioning element (s) (2) in a carton (C) is mounted along a conveyor (4) directed along a longitudinal axis (Y, Y′). The packing device (1) includes a robotic cell (3) associated with a cushioning element storage zone (2), the robotic cell (3) including at least one gripping device fo a cushioning element (2). The storage zone includes at least one magazine (18) with at least one cassette (8) movable along a transverse axis (X, X′) from a loading position to an unloading position.