In an earlier work (Litvinov et al., Phys.Rev.E 77, 066703 (2008)), a model for a polymer molecule in solution based on the smoothed dissipative particle dynamics method (SDPD) has been presented. In the present paper, we show that the model can be extended to three-dimensional situations and simulate effectively diluted and concentrated polymer solutions. For an isolated suspended polymer, calculated static and dynamic properties agree well with previous numerical studies and theoretical predictions based on the Zimm model. This implies that hydrodynamic interactions are fully developed and correctly reproduced under the current simulated conditions. Simulations of polymer solutions and melts are also performed using a reverse Poiseuille flow setup. The resulting steady rheological properties (viscosity, normal stress coefficients) are extracted from the simulations and the results are compared with the previous numerical studies, showing good results.