One of the interesting features of viscoelastic flow simulations is the prediction of extrudate swelling, which can be larger than its Newtonian counterpart. However, running complex 3D flows with a rheologically sophisticated model can sometimes be computationally expensive. Hence, we propose hereafter a simplified approach, which should enable the qualitative prediction of the extrudate free surface. This approach can be referred to as the "simplified viscoelastic model", or "light viscoelastic model". The suggested model is also sometimes referred to as the acronym "ScaFTen", which is the name of a research project that stands for "Scalar For Tensor".