The branched polymer melts are modeled respectively in this investigation by the existing XPP and PTT-XPP models, along with the proposed S-MDCPP (Single/Simplified Modified Double Convected Pom-Pom) model developed on the basis of the existing MDCPP model A pressure stabilized mass equation is formulated with the finite increment calculus (FIC) process to restrain and further eliminate spurious oscillations of pressure field due to the incompressibility of fluids. The discrete elastic viscous stress splitting (DEVSS) technique is employed, in order to retain an elliptic contribution in the weak form of the momentum equation An inconsistent streamline-upwind (SU) method is applied to spatially discretize the constitutive equations. The mass, momentum conservation and constitutive equations are discretized and solved by the iterative stabilized fractional step algorithm along with the Crank-Nicolson implicit difference scheme Thus the finite elements with equal low-order interpolation approximations for velocity-pressure-stress variables can be devised to numerically simulate the viscoelastic contraction flows for branched LDPE melts The influences of the three viscoelastic constitutive models and the branched arms at the end of the Pom-Pom molecule on the rheological behaviors occurring in this complex flow are discussed The numerical results demonstrate that the proposed S-MDCPP model is capable of reproducing some properties similar to those predicted by the XPP model in high shear flow and, on the other hand, reproducing some properties similar to those predicted by the PTT-XPP model in high elongational flow Furthermore, the proposed S-MDCPP model is capable of well identifying the macromolecule topological structures of branched polymer melts (c) 2010 Elsevier B V. All rights reserved.