Abstract: The developments of investigations on extrudate swell by usingnumerical simulation methods are reviewed in this paper. Themathematical model of extrusion swelling is given first, and thenthe studies on swelling in the last twenty years are reviewed. Thecomputational processes, the characteristics, and the results ofthe numerical methods are summarized.The authors propose their views on studying the extrudate swell and pointout problems in the reported studies and the trendof investigation on swelling.