A new extruder design has been developed for the coextrusion of two-layer annular sections. The extruder consists of a conical stator-rotor-stator assembly, which performs extrusion from each side of the rotor. Flow within this assembly is fully three-dimensional, with helicoidal streamlines in the vicinity of the rotor and the die entry region. Fiber orientation is created in a circumferential direction by these helicoidal streamlines; close to the inner and outer surfaces of the tube, the fibers are parallel to the main extrusion direction, whereas in the mid-thickness, they are oriented in the circumferential direction. It is demonstrated that the amount of orientation depends on rotor speed and die design. When using a short die and high rotor speed, an increased fraction of fibers are oriented in the circumferential direction.