Abstract: D extrudate swell of polymer melts was analyzed by the finite element method. The constitutive equation used is integral Wagner model in which the nonlinear decay function is contained, and it is generally recognized better one to describe the memory effects for polymer melts. The method used to compute the extra stresses in the constitutive model was given here. Therefore, the solution of the finite element nonlinear equations can be obtained by suitable iteration. Simultaneously, according to the boundary conditions of free surface, the final position and shape of exit free surface can also be found. Based on the above technique, as a test, the 3D extrudate swell of LDPE melt in the circular die was simulated. Results are in good agreement with those of 2D axial symmetry analysis and experimental data. Finally, the analysis of 3D extrudate swell in rectangle die was done and the extrudate shape was obtained.