With this research, we work towards the overall objective of customizing polymer molecules in terms of their molecular structure to optimize processing performance. The work includes analysis of the rheology in shear and shear-free flows for sparsely long-chain branched, LCB, polyethylene, PE, resins; determination of the consistency of the molecular based constitutive model, the pom-pom model; for these flows, and evaluation of the same PE resins in film-casting. As we progress towards molecular systems with defined molecular structural characteristics, we transition from a linear low density polyethylene, LLDPE, based series of PE resins to a high density polyethylene, HDPE, based series of PE resins, each with materials of varying degrees of sparse LCB. Evaluation of the shear step-strain rheology for the series of LLDPE-based PE resins allows for the assessment of any inadequacies associated with the step-strain experiments and the ability of the K-BKZ analog of the pom-pom constitutive model to predict step-strain rheological behavior. Finite rise time and wall slip are addressed to ensure the accuracy of the experimental step-strain measurements and eliminated as factors contributing to the stress relaxation moduli response. Analysis of the K-BKZ analog of the pom-pom constitutive model includes comparisons between experimental stress relaxation moduli and predictions from the model using pom-pom model parameters determined from extensional rheology. The results show inconsistencies in the model predictions, where the predictions fail to capture the short time behavior and accurately dampen at larger strains. Pom-pom model parameters are determined using the K-BKZ analog of the pom-pom constitutive model and fitting the stress relaxation moduli. These results are qualitatively consistent indicating that branching occurs on the longest backbone segments, but the values appear to be unrealistic with respect to the molecular theory. Analysis of film-width reduction or necking during film-casting for the series of LLDPE-based resins determines whether uniaxial extensional rheological characteristics, in particular strain-hardening, that are a result of LCB influence the film-necking properties. At the lowest drawdown ratio necking is observed to be reduced with increasing LCB, and thus strain-hardening characteristics. At the higher drawdown ratios it is observed that LCB no longer reduces necking and the curves merge to the results found for linear PE, except in the case of LDPE, which shows reduced necking at all drawdown ratios. Furthermore, comparisons of film necking are also made to separate the effects of molecular weight distribution, MWD, and LCB. The results indicate that both broadening the MWD and the addition of sparse LCB reduce the degree of necking observed. It is established that film necking is more significantly reduced by LCB than by broadening the MWD. Analysis of the uniaxial extensional and dynamic shear rheology with the pom-pom constitutive model reveals that a distribution of branches along shorter relaxation time modes is important in reducing necking at higher drawdown ratios. Factors such as shear viscosity effects, extrudate swell, and non-isothermal behavior were eliminated as contributing factors because of the similar shear viscosity curves, N1 curves, and activation energies among the sparsely LCB PE resins. The same experimental concepts have been extended to the series of HDPE-based resins, but the lack of adequate uniaxial extensional data prevents a thorough analysis with respect to uniaxial extensional characteristics. Regardless, in the context of step-strain rheology, the results were found to be similar with those of the LLDPE-based series of resins, where a distinctive shape at short times was observed for any of the PE resins possessing some level of LCB that was not apparent in the linear PE resins. Film-casting revealed similar results to those of the LLDPE-based materials as well, but a broader spectrum of drawdown ratios revealed greater insight into how the distribution of branching controls the film-casting response. At low drawdown ratios all materials exhibit the same necking behavior. At intermediate drawdown ratios separation occurs where the linear PE resins experiences the most drastic necking, the sparsely LCB PE resins show reduced necking, and the LDPE shows an even greater reduction in necking. Progression then to the higher drawdown ratios results in similar necking behavior for the linear and sparsely LCB PE resins and greatly reduced necking for the LDPE. These results support the idea that to reduce necking the backbone segments that dominate the film-casting behavior must contain some level of LCB. / Ph. D.