The molecular structure of two different types of industrial low-density polyethylenes (LDPE), i.e., tubular and autoclave, was investigated by gel permeation chromatography and different rheological methods and then compared with predictions from theoretical modeling. Linear rheological data generated from small amplitude oscillatory shear (SAOS) are presented using the framework of a Van Gurp-Palmen plot while nonlinear rheological data obtained from either transient shear, transient extension, or medium amplitude oscillatory shear (MAOS) are compared with simulations using a generalized form of the molecular stress function theory with only three nonlinear material parameters: a(2), beta, and f(max) which represent the dissipation in simple shear flow, the ratio of molar mass of the branched polymer to the molar mass of the backbone, and the maximum stretching of the polymer chain before chains slip past one another without further stretch, respectively. The effect of these parameters on the predictions is investigated for the aforementioned nonlinear deformations. As a result of these comparisons, a(2) was found to have a constant value within experimental error (a(2) = 0.07 +/- 0.03) when simulating the shear stress growth coefficient. Next, beta was defined by fitting the extensional data with this model resulting in a constant value of 1.8 for tubular LDPEs and a value between 1.6 and 2.1 for autoclave LDPEs depending on the molecular structure. The universality of these beta values was found by simulating the intrinsic nonlinearity Q(0)(omega)equivalent to lim(gamma 0) ,I-0(3/1/)gamma(2)(0) (defined by Fourier transform rheology method) in the MAOS region. Finally, f(max) was evaluated by fitting the model to tensile stress growth coefficient data. It was found that f(max) is independent of the extensional rate for tubular LDPEs but exhibits a power law behavior with the extensional rate for autoclave LDPEs. Our investigations demonstrated that nonlinear deformations instead of SAOS deformations are the preferred method for characterizing the molecular structure of these polymers due to its sensitivity to the complex structure of LCB present in these materials along with their broad molecular weight distribution. (C) 2013 The Society of Rheology.