Screw extruder for the continuous extrusion of materials with high viscosity, in particular metals such as aluminium and its alloys. The extruder includes an Archimedes screw (1) rotationally providedwithin liner (2) of a screw housing (4) with an inlet (11) for the feeding of the material to be extruded, a compacting or extrusion chamber (5) and an extrusion die assembly with a die (6) which forms the shape of the desired extruded product (7). The design of the screw (1) and liner (2) is such that the required compaction takes place at the down-stream end of the screw towards the extrusion chamber (5) corresponding to up to 540 DEG of the rotation of the screw, or up to 1.5 turn of the screw flight length, and that the solid plug of metal thus formed at the end of the screw and extrusion chamber (5) is restricted from rigid rotation to obtain the required compaction and extrusion pressure.