Tube tooling extrusion coating is simulated for a low density polymer melt using a finite element method and a single-mode exponential Phan-Thien/Tanner constitutive model. A time-stepping Taylor-Galerkin/pressure-correction scheme is used under both coupled and decoupled solution approaches. Stress response and pressure drop across the flow are investigated. For longer relaxation times, shear and tensile stress do not vary significantly throughout the flow, whilst pressure drop is found to be most sensitive to the quality of the model fit to the shear experimental data.