The hierarchical multi‐mode molecular stress function (HMMSF) model developed by Narimissa and Wagner [Rheol. Acta 54, 779–791 (2015), and J. Rheol. 60, 625–636 (2016)] for linear and long‐chain branched (LCB) polymer melts were used to analyze the set of transient elongational and shear viscosity data of two LCB low‐density polyethylenes (1840H and 2426 k), and a linear poly‐(ethylene‐co‐α‐butene), PEB A‐780090 as reported by [Li et al. J. Rheol. 64, 177 (2020)], who had developed a new horizontal extensional rheometer to extend the lower limits of elongational viscosity measurements of polymer melts. Comparison between model predictions and elongational stress growth data reveals excellent agreement within the experimental window, and good consistency with shear stress growth data, based exclusively on the linear‐viscoelastic relaxation spectrum and only two nonlinear model parameters, the dilution modulus GD for extensional flows, and in addition a constraint release parameter for shear flow.