The paper is concerned with the numerical prediction of the flow of polymer melts using a pom-porn model [J. Rheol. 42 (1998) 81]. The pom-porn model is a coarse-grained molecular model that was developed for describing branched polymers. A description of the configuration distribution is given in terms of the orientation and stretch of the pom-pom molecule. The variant of the pom-porn model used in this paper is the extended pom-pom model [J. Rheol. 45 (4) (2001) 823]. The model has been rewritten to make it suitable for implementation in an existing spe=al element algorithm, which solves the constitutive equation together with the momentum and continuity equations The temporal discretization of the convective terms in the momentum equation and the constitutive equation is performed using a second-order time-splitting technique. Spatial discretization is performed using spectral element techniques. The system of discretized equations is solved using a preconditioned conjugate gradient method, and details of the preconditioners are given. Results are presented for the start-up of Poiseuille flow in a planar channel, and flow past a confined cylinder. The influence of the model parameters on the solution is described. (C) 2004 Elsevier B.V. All rights reserved.