A vehicle structure sub-unit, comprising - a cross-member made of metal material, including, with reference to the mounted condition on the vehicle, a front wall, a rear wall, an upper wall and a lower wall, - two crash-box modules welded or glued to the rear wall of the cross-member, near two opposite ends of the cross-member and extending in a direction parallel to the longitudinal direction of the vehicle, with reference to the mounted condition on the vehicle, starting from said rear wall of the cross-member, - each crash-box module having a tubular structure of metal material, having an upper wall and a substantially horizontal lower wall and two side walls (33, 34) substantially vertical and parallel to each other, - so that each crash-box module has a front surface shaped like a quadrangular ring, with a horizontal upper edge, a horizontal lower edge, a vertical inner edge, facing towards the center of the cross-member, and a vertical outer edge, - said front surface of the crash-box module being glued or welded to the rear wall of the cross-member, - a reinforcing metal plate being interposed between the front surface of at least one of the two crash-box modules and the rear wall of the cross-member, said mteal plate being rigidly connected by welding or gluing both to the rear wall of the cross-member and to the front surface of the crash-box module, said sub-unit being characterized in that: - the rear wall of the cross-member has a depressed flat portion in which said reinforcing plate is received, in such a way that the surface of the reinforcing plate facing the crash-box module is substantially flush with the surface of the rear wall of the cross-member adjacent to said depressed portion, - said depressed portion of the rear wall of the cross-member within which the reinforcing plate is received is located in an offset position, closer to the center of the cross-member, with respect to said crash-box module, - in such a way that the reinforcing plate is in contact with just a part of the front surface of the crash-box module, the remaining part of said front surface being in direct contact with the rear wall of the cross-member. - a cross-member made of metal material, including, with reference to the mounted condition on the vehicle, a front wall, a rear wall, an upper wall and a lower wall, - two crash-box modules welded or glued to the rear wall of the cross-member, near two opposite ends of the cross-member and extending in a direction parallel to the longitudinal direction of the vehicle, with reference to the mounted condition on the vehicle, starting from said rear wall of the cross-member, - each crash-box module having a tubular structure of metal material, having an upper wall and a substantially horizontal lower wall and two side walls (33, 34) substantially vertical and parallel to each other, - so that each crash-box module has a front surface shaped like a quadrangular ring, with a horizontal upper edge, a horizontal lower edge, a vertical inner edge, facing towards the center of the cross-member, and a vertical outer edge, - said front surface of the crash-box module being glued or welded to the rear wall of the cross-member, - a reinforcing metal plate being interposed between the front surface of at least one of the two crash-box modules and the rear wall of the cross-member, said mteal plate being rigidly connected by welding or gluing both to the rear wall of the cross-member and to the front surface of the crash-box module, - the rear wall of the cross-member has a depressed flat portion in which said reinforcing plate is received, in such a way that the surface of the reinforcing plate facing the crash-box module is substantially flush with the surface of the rear wall of the cross-member adjacent to said depressed portion, - said depressed portion of the rear wall of the cross-member within which the reinforcing plate is received is located in an offset position, closer to the center of the cross-member, with respect to said crash-box module, - in such a way that the reinforcing plate is in contact with just a part of the front surface of the crash-box module, the remaining part of said front surface being in direct contact with the rear wall of the cross-member.