The Numerical simulation was performed on the flow field around the two-dimensional rectangular bluff body in order to complement the previous experimental results of the bluff body stabilized flames [1]. For both fuel ejection configurations against an oxidizer stream, the flame stability was affected mainly by vortex structure and mixing field near bluff body. FDS(Fire Dynamic Simulator) based on the LES(Large Eddy Simulation) was employed to clarify the isothermal mixing characteristic and wake flow pattern around bluff body. The air used atmosphere and the fuel used methane. The result of counter flow configuration shows that the flow field depends on air velocity but the mixing field is influenced on the fuel velocity. At low fuel velocity the fuel mole fraction is below the flammable limit and hence the mixing is insufficient to react. Therefore, as the result, the flame formed at low fuel velocity is characterized by non-premixed flames. For the flow field of co-flow configuration, flame stability was affected by fuel velocity as well as air velocity. the vortex generated by fuel stream has counter rotating direction against the air stream. Therefore, the momentum ratio between air and fuel stream was important to decide the flame blow out limit, which is result in the characteristic of the partially premixed reacting wake near extinction.