We developed a novel Hierarchical Multi-mode Molecular Stress Function (HMMSF) model for linear and long-chain branched (LCB) polymer melts implementing the basic ideas of (1) hierarchical relaxation, (2) dynamic dilution, (3) interchain tube pressure, and (4) convective constraint release. With a minimum number of nonlinear free parameters and remarkable quantitative predictions of the rheology of polymer melts, this model is an outstanding option for the simulation of different processing operations in the polymer industry. The excellent predictions of this model were demonstrated in uniaxial, equibiaxial, and planar extensional deformations for linear and LCB melts, as well as in shear flow for a LCB polymer, with a minimum number of adjustable free nonlinear material parameters, that is, one in the case of extensional flows, and two in shear flow. In this contribution, we review the development of the HMMSF model and present a reduced number of well-defined constitutive relations comprising the rheology of both linear and LCB melts. We also extend the comparison of model and data to cover the shear flow of a linear polymer melt. POLYM. ENG. SCI., 59:573–583, 2019.