Abstract: A process and a machine for overpacking luggage of users of different transport means and in particular, for airplane passengers.The machine includes a device for forming a packing around each luggage (5), moving the luggage upon a conveyor belt (8) and during its movement, providing the packing in the form of a protecting envelope (16) made of a plastic material, while providing the envelope (16) with an opening extending in front of the handle (6).