The Two Coupled Maxwell Modes (TCMM) Model is applied to give quantitative descriptions of shear-thickening behavior, which can be observed under certain conditions for high molecular weight polymers dissolved in low viscosity solvents. The TCMM Model is written in terms of five parameters representing the relaxation time of each mode, the concentration of each mode, and a coupling parameter between the two modes. Using all of the available experimental data for steady-shear viscosity and dichroism we found in the literature, we performed a full parameterization of these five quantities. Furthermore, from this parameterization we can describe the functional dependencies of the relaxation times, modal concentrations, and coupling parameter as functions of temperature, concentration, and molecular weight of the polymer. These functional dependencies are explained in light of the underlying physics imbedded in the TCMM Model. We demonstrate that by optimizing to only the viscosity data, we were able to obtain the same relaxation times, modal concentrations, and coupling parameter as using both the viscosity and dichroism data. This is useful because typically the experimental dichroism data is not available. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 90: 2997–3011, 2003