An Extruder for shaping a viscous material such as a blend of rubber is disclosed herein. The extruder includes a screw rotationally driven about an axis (XX′) in a barrel and bearing one or more helical flights extending radially outwards from a central shaft of the screw, the extruder comprising a material homogenization zone (H) through which a screw portion comprising interrupted flight elements forming empty annular spaces extends axially, and a barrel portion delimiting the said homogenization zone bearing flight elements extending radially inwards into the said empty annular spaces. According to the disclosure, the barrel portion delimiting the homogenization zone is itself rotationally driven about the axis XX′ to form a rotary barrel.