Stable and accurate spectral element methods for predicting the flow of branched polymer melts past a confined cylinder are presented. The fluid is modelled using a modification of the pom-pom model known as the extended pom-pom (XPP) model. Steady and transient flows are considered in this paper. The operator integration factor splitting technique is used to discretize the governing equations in time, while the spectral element method is used in space. An iterative solution algorithm that decouples the computation of velocity and pressure from that of stress is used to solve the discrete equations. Appropriate preconditioners are developed for the efficient solution of these problems. Local upwinding factors are used to stabilize the computations. Numerical results are presented demonstrating the performance of the algorithm and the predictions of the model. The influence of the model parameters on the solution is described and, in particular, the dependence of the drag on the cylinder as function of the Weissenberg number. (c) 2005 Elsevier B.V. All rights reserved.