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The properties of semidilute polymer solutions are investigated at equilibrium and under shear flow by mesoscale simulations, which combine molecular dynamics simulations and the multiparticle collision dynamics approach. In semidilute solution, intermolecular hydrodynamic and excluded volume interactions become increasingly important due to the presence of polymer overlap. At equilibrium, the dependence of the radius of gyration, the structure factor, and the zero-shear viscosity on the polymer concentration is determined and found to be in good agreement with scaling predictions. In shear flow, the polymer alignment and deformation are calculated as a function of concentration. Shear thinning, which is related to flow alignment and finite polymer extensibility, is characterized by the shear viscosity and the normal stress coefficients.