In this paper the two-dimensional and unsteady laminar free stream flow across a circular cylinder in different Reynolds numbers has been investigated. The formations of vortex shedding behind the circular cylinder under uniform and fluctuating flow are simulated. The strength of the re-circulating wake for the steady flow regime and also for the Strouhal frequency of vortex shedding are numerically calculated. Also the effect of grid sensitivity and decrease in boundary condition domain are numerically calculated. The results were shown good agreement between the numerical simulation and Thompson’s experimental data. The global quantities such as drag coefficients, Strouhal number and the detailed kinematic variables like stream function, vorticity and so on, have been obtained for the above range of conditions

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