The theology and configurational properties of dilute polymer solutions in steady shear flow are modeled by dissipative particle dynamics (DPD), a new mesoscopic simulation method. The simulations represent the polymer as a 10-bead chain of FENE connector springs and the solvent as a sea of free DPD particles. Thermodynamic interactions between the polymer and solvent are modeled by varying the strength of the repulsive forces acting between unlike particle species. Since DPD simulations model the full hydrodynamics of the polymer-solvent system, instantaneous hydrodynamic interactions among beads of the polymer chain emerge naturally from the simulations. The predicted rheological material functions include realistic features such as shear thinning of the viscosity and first normal stress coefficient, and negative values for the ratio psi(2)/psi(1). The enhancement of eta, psi(1), and psi(2) by means of chain expansion in good solvents is also realistically represented by the model predictions. The DPD, simulations accurately describe the variation of the orientation angle of polymer chains with the shear rate, and predict macromolecular expansion ratios that are in good agreement with the recent flow light scattering measurements of Lee and Muller [Polymer 40, 2501-2510 (1999)].