The seminal ideas. of de Gennes and Doi and Edwards have provided the theoretical framework for much of the recent effort to model the rheological behavior of entangled polymer melts and solutions. Recent theoretical work has incorporated a number of important additions to the basic Doi-Edwards theory, including an explicit description of chain stretch and additional relaxation mechanisms such as contour length fluctuations (CLF) and convective constraint release (CCR). However, very little quantitative data has been published on the rheological behavior of entangled systems in strong flows. Hence, a comprehensive examination of the theoretical developments has not been possible. The experiments described in this paper use the filament stretching rheometer to obtain transient extensional stress growth data and steady state uniaxial extensional viscosity data for a number of entangled, narrow molecular weight distribution polystyrene solutions in the strain-rate regime characterized by a significant degree of both chain alignment and stretch. These results are then compared with theoretical predictions for a number of the current generation of reptation-based models, including mechanisms for chain stretching, contour length fluctuations, and convective constraint release. These comparisons demonstrate that when the model parameters are properly obtained from linear viscoelastic measurements, the recent model due to Mead, Larson, and Doi (Macromolecules 1998, 31, 7895) provides quantitative predictions for this class of flows for solutions spanning the complete range from very lightly to highly entangled. solutions.