＇＇Exact＇＇ solutions for the Hookean and FENE dumbbell models with internal viscosity have been found using Brownian dynamics simulations. Results from these two dumbbell models are compared to Liang and Mackay＇s experimental data on semidilute xanthan gum solutions. We find that the FENE dumbbell model predicts very well Liang and Mackay＇s measurements on the dissipative and elastic contributions to shear stress. For the Hookean dumbbell model, shear thickening is observed for all but very small values of the internal viscosity parameters epsilon, which is not seen by approximate methods. The Hookean dumbbell model greatly overestimates the polymer contribution to shear stress when compared with Liang and Mackay＇s experimental data, and no single value of epsilon is able to predict all of their experimental results well; both the FENE and the Hookean dumbbell models fail to predict the right form of the nonlinear relaxation modulus in the step strain experiment. On checking the Gaussian approximation method of the Hookean dumbbell model, we find that for small values of epsilon, the approximate results show very good agreement with the Brownian dynamics simulations. For larger values of epsilon, deviations are seen at high shear rates. Nevertheless, the initial oscillation of shear stress predicted by the Gaussian approximation for large values of epsilon at high shear rates in the startup of steady shear flow is verified by the Brownian dynamics simulation, though they are much less extreme.