The ability of the multi-mode eXtended Pom-Pom model to predict inhomogeneous flows ofa polyethylene melt is investigated. Two benchmark problems are examined: the confined flowaround a cylinder, and the flow through a cross-slot device. Numerical results for the eXtendedPom-Pom model are compared to experimental data, and predictions of the Giesekus and expo-nentialPhan-Thien Tanner (PTT-a) models. Characteristic features observed experimentally in thebenchmark flows are described well by all three models. The eXtended Pom-Pom model performsmost satisfactorily, both with respect to the rheological data and the inhomogeneous flow data.