Process for manufacturing a muffler assembly unit for an exhaust system of an internal combustion engine, comprising the steps: a) Provision of a muffler with a muffler housing with a circumferential wall elongated in the direction of a housing longitudinal axis, b) Provision of a housing jacket for the muffler housing with a jacket contour adapted to an outer circumferential contour of the circumferential wall and with a connecting edge for connecting the housing jacket to the circumferential wall, wherein the step b) comprises: a step b1) for the provision of a plate-like sheet metal blank for a jacket body, a step b2) for reshaping the sheet metal blank such that the jacket body having a shell-like shape is provided with a body bottom, with a body circumferential wall and with the connecting edge at the body circumferential wall, wherein in step b2) the sheet metal blank is reshaped such that in at least one jacket body segment (34, 36, 38) the connecting edge extends essentially along the entire body circumferential wall provided thereon and that at least two jacket body segments (34, 36, 38), which merge into each other in a jacket bending area (40, 42) elongated in the direction of a bending line (L 1, L 2), are formed, wherein the body circumferential wall is interrupted in at least one jacket bending area (40, 42) and the jacket body segments (34, 36, 38) are connected to one another essentially only by the body bottom, a step b4) for the arrangement of insulating material at the jacket body by inserting the insulating material into the jacket body with a shell-like shape, c) arrangement of the housing jacket in a connecting position enclosing the circumferential wall of the muffler housing in some areas such that the connecting edge abuts at the circumferential wall, and d) permanent connection of the connecting edge of the housing jacket to the circumferential wall of the muffler housing by welding. a) Provision of a muffler with a muffler housing with a circumferential wall elongated in the direction of a housing longitudinal axis, b) Provision of a housing jacket for the muffler housing with a jacket contour adapted to an outer circumferential contour of the circumferential wall and with a connecting edge for connecting the housing jacket to the circumferential wall, wherein the step b) comprises: a step b1) for the provision of a plate-like sheet metal blank for a jacket body, a step b2) for reshaping the sheet metal blank such that the jacket body having a shell-like shape is provided with a body bottom, with a body circumferential wall and with the connecting edge at the body circumferential wall, wherein in step b2) the sheet metal blank is reshaped such that in at least one jacket body segment (34, 36, 38) the connecting edge extends essentially along the entire body circumferential wall provided thereon and that at least two jacket body segments (34, 36, 38), which merge into each other in a jacket bending area (40, 42) elongated in the direction of a bending line (L 1, L 2), are formed, wherein the body circumferential wall is interrupted in at least one jacket bending area (40, 42) and the jacket body segments (34, 36, 38) are connected to one another essentially only by the body bottom, a step b4) for the arrangement of insulating material at the jacket body by inserting the insulating material into the jacket body with a shell-like shape, a step b1) for the provision of a plate-like sheet metal blank for a jacket body, a step b2) for reshaping the sheet metal blank such that the jacket body having a shell-like shape is provided with a body bottom, with a body circumferential wall and with the connecting edge at the body circumferential wall, wherein in step b2) the sheet metal blank is reshaped such that in at least one jacket body segment (34, 36, 38) the connecting edge extends essentially along the entire body circumferential wall provided thereon and that at least two jacket body segments (34, 36, 38), which merge into each other in a jacket bending area (40, 42) elongated in the direction of a bending line (L 1, L 2), are formed, wherein the body circumferential wall is interrupted in at least one jacket bending area (40, 42) and the jacket body segments (34, 36, 38) are connected to one another essentially only by the body bottom, a step b4) for the arrangement of insulating material at the jacket body by inserting the insulating material into the jacket body with a shell-like shape, c) arrangement of the housing jacket in a connecting position enclosing the circumferential wall of the muffler housing in some areas such that the connecting edge abuts at the circumferential wall, and d) permanent connection of the connecting edge of the housing jacket to the circumferential wall of the muffler housing by welding.