An apparatus (10) suitable for processing a heterogeneous stream of waste material comprising: a housing (11) having a compaction compartment (19); a screw vane (20), located in the compaction compartment, for processing and transporting the waste material through the compaction compartment. The screw vane having a shaft (20b) about which is located a flight (20a) which extends radially outwardly in the form of a helical thread along the length of the shaft. The apparatus further comprises a heating zone (31) having a heating source (32), which is located adjacent to the housing and receives processed waste that has exited the compaction zone; and an extrusion nozzle which allows for processed waste to exit the heating zone. The diameter of the flight of the screw vane decreases along the length of the shaft towards a forward end of the shaft in cooperation with tapering of the diameter of the compaction compartment. A method for processing waste material is also provided. The apparatus and method advantageously provide output waste material which retains its compacted form and does not re-expand to its pre-compressed state.