The co-kneader is a particular single-screw extruder with pins fixed on the barrel, interrupted screw flights, and a screw with both rotational and reciprocating motions. The co-kneader is principally used for its excellent mixing capacities. In order to calculate the flow in the co-kneader, we developed a simplified Hele-Shaw model which takes into account the mixing pins and the reciprocating motion of the screw. In this paper we describe the model and the effects of the reciprocating motion and the presence of mixing pins on the polymer flow.