The paper presents numerical simulations of laminar vortex-shedding flows past a circular cylinder for Re ≤ 500. The simulations are performed by solving the unsteady 2-D Navier-Stokes equations with a finite volume method using unstructured grid system. The resulting Reynolds number dependence of the Strouhal number and of the drag and lift coefficients is compared with experiments and with previous numerical results, showing good agreement. It is found that, for the truly laminar Reynolds number range the present calculation method described is capable of producing reasonably accurate results for the main practically relevant parameters such as Strouhal number, drag and lift coefficients.