The nonlinear transient extensional and steady-state shear theological properties of dilute polystyrene solutions of molecular weight 3.9 and 10.2 million in a theta solvent are predicted using Brownian dynamics (BD) simulations with the bead-spring model. Full hydrodynamic interaction is incorporated into BD simulations using the Rotne-Prager tensor. The hydrodynamic interaction parameter h* is obtained a priori by matching the drag force from a fully extended bead-spring model in extensional flow with that from Batchelor's theory for a cylindrical rod [Hsieh et al. (2003)]. The agreement between experimental data [Gupta et al. (2000)] and simulation results for the transient Trouton ratio versus strain is good from low to medium strains. However, the plateaus at high strains predicted by the simulations are higher than measured. We also find that hydrodynamic interaction hinders the unraveling of a polymer chain in strong extensional flow (Wi much greater than 1) due to the hydrodynamic clustering of beads. In steady shear flows, the combination of hydrodynamic interaction and finite spring extensibility results in a shear-thinning-thickening-thinning behavior with an increasing shear rate. For polystyrene of molecular weight 3.9 million, the simulated first normal stress coefficient does not quantitatively match the experimental results, in part because the number of beads N required to represent the hydrodynamic interactions accurately exceeds N = 300, which is much higher than we can afford to use, namely N = 80. We also predict a negative value of the second normal stress coefficient. (C) 2004 The Society of Rheology.