A novel hierarchical multi-mode molecular stress function (HMMSF) model for long-chain branched (LCB) polymer melts is proposed, which implements the basic ideas of (i) the pom-pom model, (ii) hierarchal relaxation, (iii) dynamic dilution and (iv) interchain pressure. Here, the capability of this approach is demonstrated in modelling uniaxial extensional viscosity data of numerous broadly distributed long-chain branched polymer melts with only a single non-linear parameter, the dilution modulus.