Extrudate swell is a common phenomenon in the polymer processing. The investigation of its mechanism has both scientific and industrial interest. In the study, the swell phenomenon of LDPE flowing through annular extrusion die is investigated by using finite element simulation. The effects of die geometry on the annular extrudate swell and on the polymer flow patterns are discussed in detail. The rheology of LDPE is described by using viscoelastic PTT (Phan-Thien-Tanner) constitutive model and the corresponding material parameters are obtained by fitting the material functions detected on a strain-controlled rheometer. The mathematical model of annular extrudate swell is established and its finite element model is derived in the study. A penalty method is employed to solve the extrudate swell problem with a decoupled algorithm. The computation stability is improved by using the discrete elastic-viscous split stress (DEVSS) algorithm with the inconsistent streamline-upwind (SU) scheme. The essential flow characteristics of polymer melts flowing through annular extrusion die with different die contraction angles, different ratios of parallel length to inner radius, and different ratios of outer to inner radius are then predicted by using the proposed numerical method and the mechanism of swell phenomenon is further discussed. (C) 2010 Wiley Periodicals, Inc. J Appl Polym Sci 117: 91-109,2010