Abstract: Sound damping apparatus for internal combustion engines, especially for public works or agricultural machines, and machines provided with such an apparatus.This sound damping device is intended for machines or engines mounted within a bonnet (1) and provided with a blower (3) discharging cooling air to the outside through a radiator (4). It is constituted by a sound damping element (9, 21) such as a block of expanded foam material having one or more central openings (14) oriented in the direction of flow of the air discharged by the blower and peripheral openings (16) inclined or specially shaped so as to direct the air towards the central flow passing through the central opening or openings downstream of the device. Means are provided for forming an expansion chamber (13) between the radiator and the sound damping element.