System for covering a luggage compartment of a motor vehicle, said system comprising: • a screen for covering said compartment having a first and a second face, • attachment means disposed on the lateral edges of said screen, • reciprocal attachment means provided in the lateral portions of said compartment, so as to allow for an assembly in transversal tension of said screen to place it in covering configuration, said system being characterised in that said means comprise: • an elastic link a first end of which is provided with a first endpiece and a second end of which is provided with a second endpiece, said second endpiece being in the form of a profile provided at its free end with a collar, • a first shell thrust at the edge of said screen on said first face, the interior of said shell being provided with a means for anchoring said first endpiece, said shell being furthermore provided with a first transversal protrusion in the form of a gutter matching the shape of said second endpiece, said endpiece being slidably mounted in said protrusion, said collar abutting against the free end of said protrusion when said link is not solicited in traction, • a second shell thrust at the edge of said screen on said second face in such a way as to close said first shell with interposition of said screen between the two, said second shell being furthermore provided with a second transversal protrusion closing said first protrusion in such a way as to form with it a sleeve for slidably receiving said second endpiece, • means for fastening said shells on said screen, and in that said reciprocal means have a notch for receiving said sleeve, said notch having a transversal thickness similar to the length of said sleeve, said sleeve being maintained in said notch by said collar bearing against the external edge of said notch and being recalled towards the inside by said link. • a screen for covering said compartment having a first and a second face, • attachment means disposed on the lateral edges of said screen, • reciprocal attachment means provided in the lateral portions of said compartment, so as to allow for an assembly in transversal tension of said screen to place it in covering configuration, • an elastic link a first end of which is provided with a first endpiece and a second end of which is provided with a second endpiece, said second endpiece being in the form of a profile provided at its free end with a collar, • a first shell thrust at the edge of said screen on said first face, the interior of said shell being provided with a means for anchoring said first endpiece, said shell being furthermore provided with a first transversal protrusion in the form of a gutter matching the shape of said second endpiece, said endpiece being slidably mounted in said protrusion, said collar abutting against the free end of said protrusion when said link is not solicited in traction, • a second shell thrust at the edge of said screen on said second face in such a way as to close said first shell with interposition of said screen between the two, said second shell being furthermore provided with a second transversal protrusion closing said first protrusion in such a way as to form with it a sleeve for slidably receiving said second endpiece, • means for fastening said shells on said screen, and in that said reciprocal means have a notch for receiving said sleeve, said notch having a transversal thickness similar to the length of said sleeve, said sleeve being maintained in said notch by said collar bearing against the external edge of said notch and being recalled towards the inside by said link.