Abstract: A rotary drum 2 is provided with vanes 26 extending longitudinally thereof defining passages 21 therebetween with gas to be fed to the reactor being fed only to those of the passages 21 the outlets from which into the reactor are covered by the solid material 20 being tumbled therein. Within this arrangement it can be ensured that the hot gases being used to treat the solid materials can be passed through the solid material as it is being tumbled in the reactor with the reactor being capable of accepting a large range of different materials with a variation of particle and lump size. The reactor in its preferred exemplary form is used for starved air incineration of waste materials, the gas supply means being used to supply gas in an amount insufficient to complete the reaction in the drum such that combustible gases leave the outlet end for use in the burner 10 used to provide the hot gases to the reactor drum.