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In this study prediction of the steady-state flow of branched polymer melts in pipe geometry with finite volume method is presented. The fluid is modelled using a modification of the Pom-Pom model known as the single eXtended Pom-Pom (XPP) where viscoelastic fluid, is typically a commercial low-density polyethylene. In finite volume method, the operator-integration is used to discretize the governing equations in space or control volume. An iterative solution algorithm that decouples the computation of momentum from that of stress is used to solve the discrete equations. Numerical results are presented; include the profiles of all relevant stresses, the axial velocity, stretch and the viscosity across the gap, demonstrating the performance of the model predictions. The influence of the model parameters on the solution and flow behaviour is described and, in particular, the dependence of velocity and stresses distribution as a function of Weissenberg number is analyzed. Finally, for rectitude and accuracy, the verification of this model is performed with the Gieskus model that shows good conformity between the results.