Nonequilibrium molecular dynamics (NEMD) simulations of a dense liquid composed of linear polyethylene chains were performed to investigate the chain dynamics under shear. Brownian dynamics (BD) simulations of a freely jointed chain with equivalent contour length were also performed in the case of a dilute solution. This allowed for a close comparison of the chain dynamics of similar molecules for two very different types of liquids. Both simulations exhibited a distribution of the end-to-end vector, vertical bar R-ete vertical bar, with Gaussian behavior at low Weissenberg number (Wi). At high Wi, the NEMD distribution was bimodal, with two peaks associated with rotation and stretching of the individual molecules. BD simulations of a dilute solution did not display a bimodal character; distributions of vertical bar R-ete vertical bar ranged from tightly coiled to fully stretched configurations. The simulations revealed a tumbling behavior of the chains and correlations between the components of R-ete exhibited characteristic frequencies of tumbling, which scaled as Wi(-0.75). Furthermore, after a critical Wi of approximately 2, another characteristic time scale appeared which scaled as Wi(-0.63). Although the free-draining solution is very different than the dense liquid, the BD simulations revealed a similar behavior, with the characteristic time scales mentioned above scaling as Wi(-0.68) and Wi(-0.66).