A processing method for automatically opening a slide-open package of tobacco articles with a hinged lid; the processing method including the steps of: mechanically clamping an outer container of the package; exerting pull on the lid to rotate the lid into an open position by means of a first actuator, which contacts a top wall of the lid, and has a suction head which engages the top wall by suction; and, simultaneously and in coordination with the step of exerting pull on the lid, exerting thrust on an inner container of the package, to slide the inner container axially with respect to the outer container, by means of a second actuator, which contacts a wall of the inner container through a window formed through a corresponding wall of the outer container.