Machine and method for producing substantially cylindrical articles of the tobacco processing industry; a material with cavities is fed, along a given path, through an insertion station, where powder material is inserted into the cavities, so as to obtain a strand, and through a wrapping station, in the area of which a strip is wrapped around the strand; the powder material is inserted into each cavity by a relative insertion unit, which moves in a synchronous manner along a coupling portion of the given path.