The Pom-Pom model, recently introduced by McLeish and Larson [J. Rheol. 42, 81-110 (1998)], is a breakthrough in the field of viscoelastic constitutive equations: With this model, a correct nonlinear behavior in both elongation and shear is accomplished. The original differential equations, improved with local branch-point displacement, are modified to overcome three drawbacks: solutions in steady state elongation show discontinuities, the equation for orientation is unbounded for high strain rates, the model does not have a second normal stress difference in shear. The modified extended Pom-Pom model does not show the three problems and is easy for implementation in finite element packages, because it is written as a single equation. Quantitative agreement is shown with experimental data in uniaxial, planar, equibiaxial elongation as well as shear, reversed flow and step-strain for two commercial low density polyethylene (LDPE) melts and one high density polyethylene (HDPE) melt. Such a good agreement over a full range of well defined rheometric experiments, i.e., shear, including reversed flow for one LDPE melt, and different elongational flows, is exceptional.