There is disclosed a mouth piece, filter element or cooling element for an aerosol generating article comprising: a first section comprising a longitudinally extending core of filtering material having an outer surface and an inner surface, the inner surface defining a channel extending longitudinally from an end of the first section; a second section comprising a longitudinally extending core of filtering material; wherein the first section and the second section are adjacent and integral; wherein the channel has a non-circular transverse cross section which varies in the longitudinal direction by rotating about a longitudinal axis of the first section.