We developed a novel Hierarchical Multi-mode Molecular Stress Function (HMMSF) model for poly-disperse polymer melts, which implements the basic ideas of (i) hierarchical relaxation, (ii) dynamic dilution, and (iii) interchain tube pressure. Here, the capability of this approach is demonstrated by comparison of predictions of the HMMSF model with uniaxial extensional viscosity data of sixteen different grades of high and low density polyethylene melts, as well as two different polystyrene melts with defined topology. The modelling is solely based on the linear-viscoelastic relaxation modulus with only one non-linear material parameter, the dilution modulus. (C) 2016 Elsevier Ltd. All rights reserved.