The precise prediction of extrudate swell is significant to the control of melt flow and the quality of final products. A mathematical model of power law flow for polymer extrusion is investigated. The penalty function formulation is introduced to the finite element model and the free surface is updated with streamline equation in a decoupled method. A proper penalty constant is determined by comparison of numerical results with different penalty constants. The velocity field is obtained and the distribution of velocity on different cross sections is compared. The effects of volumetric flow rate and die shape on extrudate swell ratio are discussed. The simulation results are very important for the process and die design of the polymer extrusion.