In an automatic machine for processing tobacco articles, and having a supporting frame having a vertical front wall, at which are located a number of operating devices located along a production line for processing a succession of articles, an inner first casing is provided which can be opened and covers at least some of the operating devices, and an outer second casing is provided which can be opened, is independent of the inner first casing, and covers at least part of the inner first casing in the form of a shell; the outer second casing has a front panel facing the vertical front wall of the frame and movable, with respect to the frame, between a closed or bottom limit position, in which the front panel contacts the floor supporting the frame and is separated from the inner first casing by a distance defining the depth of a soundproofing air chamber, and an open or top limit position, in which the front panel exposes and permits access to the vertical front wall of the frame and the inner first casing.