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We consider the effects of concentration on the structural and rheological properties of dilute polymer solutions via the use of Brownian dynamics simulations. The model used here is that of Jendrejack et al. [J. Chem. Phys. 116, 7752–7759 (2002)] for -phage DNA under good solvent conditions, which incorporates excluded volume and hydrodynamic interaction effects, and has been shown to quantitatively predict the nonequilibrium behavior of the molecule in the dilute limit. Our work covers the entire dilute regime, with selected investigations into the semidilute regime, as well as spanning multiple decades of both shear and extensional flow rates. In simple shear flow, as much as a 20% increase in chain extension and 30% increase in the reduced polymer viscosity is observed at the overlap concentration, as compared to the infinitely dilute case. Additionally, predicted shear viscosities are in very good agreement with experimental observations. In elongational flow, we observe much stronger concentration dependences than in shear, with a 110% increase in chain extension and 500% increase in reduced viscosity when results are compared at equivalent extension rates. Significant concentration effects are observed at concentrations as low as 10% of the overlap concentration and are largely the result of interchain hydrodynamic interactions. ©2006 The Society of Rheology