Control of vortex shedding leads to a reduction in theunsteady forces acting on the bluff bodies and can significantlyreduce their vibrations. In this paper, the finite volume method(FVM) is used to simulate the flow around and through twodimensionalcircular obstacle. An external magnetic field isapplied to control the wake behind the obstacle and also tosuppress the vortex shedding phenomena. Maxwell equations areapplied to provide the coupling between the flow field and themagnetic field. The range of Stuart (N) and Reynolds (Re)numbers are 0-10 and 1-200, respectively. The effects ofmagnetic field on control of wake structure behind the obstacleare investigated in details. It is found that for higher Stuartnumber (i.e. N=5), drag coefficient increases rapidly by usingmagnetic field.