Vortex-shedding flows past a circular cylinder for 200≤ Re ≤ 5000 are numerically simulated with the PowerCFD code, using a finite volume method and an unstructured grid system, developed by the author. The simulation is peformed by solving the unsteady 2-D Wavier-Stokes equations with both no model and turbulence model. The resulting Reynolds number dependence of the Strouhal number and of the drag and lift coefficients is compared with both experiments and previous numerical results. It is found that, in the range of 200≤ Re ≤ 5000 the calculation method with a turbulence model is capable of producing reasonably more accurate results than that with no model for the main practically relevant parameters such as Strouhal number, drag and lift coefficients.