A machine for making sub-units of smoking articles includes a conveyor, a feed unit and an applicator. The conveyor conveys a succession of tubular segments transversely along a conveying direction. The feed unit feeds and conveys a continuous web and advances the web along a feed direction parallel to the conveying direction of the tubular segments so that the web faces respective application ends of the tubular segments. The applicator is movable along an application direction parallel to an axis of predominant extension of the succession of tubular segments and is configured to engage the web so as to separate respective closing elements from it. The applicator is also configured to apply the closing element internally or externally on an application end of a respective tubular segment in such a way as to form a closing wall to at least partly close the application end.