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