An Extruder for providing a flow of viscoelastic material such as rubber is disclosed herein. The extruder includes several zones (A, P, H, S), each assigned to a particular rheological function and arranged axially from an upstream end to a downstream end of the extruder and having an endless screw of given diameter (D). In each of the zones, at least one helicoidal flight extends radially from a central shaft of the screw over a height (h1), in a direction and with a pitch which are defined for each of the zones, and which is rotationally driven about an axis (XX′) in a barrel. The barrel is provided with various structures to further assist with the flow of the viscoelastic material