The exhaust chamber for a motor vehicle exhaust line includes: a main envelope defining a main enclosure and having an exhaust gas inlet and an exhaust gas outlet; and at least one saucer-shaped shell having an opening defined by a peripheral edge of the shell, the or each shell being tightly connected to an outside surface of the main envelope along the peripheral edge, the shell, with the main envelope, defining a secondary enclosure. The main envelope has, beneath the shell, a plurality of perforations for placing the main enclosure in communication with the secondary enclosure. The main envelope has, in a first area located beneath the shell, at least one slot for increasing the elasticity of the first area, and/or the main envelope has, in a second area that is not covered by the shell, at least one rib for increasing the stiffness of the second area.