A steady approach flow around a circular cylinder is investigated by using a large eddy simulation (LES) with the Smagorinsky subgrid-scale model. A second-order accurate in time fractional-step method and a combined finite-difference/spectral approximation are employed to solve the filtered three-dimensional incompressible Navier-Stokes equations. To demonstrate the viability and accuracy of the method, we present results at Reynolds numbers of 100, 3 × 103 , 2 × 104 , and 4.42 × 104 . At Re = 100, the physical flow is two-dimensional and the calculation is done without use of the LES method. For the higher values of Re, the flow in the wake is three-dimensional and turbulent and the LES method is necessary to describe the flow accurately. Calculated values of lift and drag coefficients and Strouhal number are in good agreement with the experimentally determined values at all of the Reynolds numbers for which calculation was done.