In this study, transverse magnetic electromagnetic plane wave scatterings by rectangular cylinders have been analyzed by a high frequency asymptotic method. Scattering field can be generated by the equivalent electric and magnetic currents which are obtained approximately from the geometrical optics (GO) fields. Our formulation is found to be exactly the same with the physical optics (PO) for the conducting cylinders, and it can also be applicable for dielectric cylinders. Numerical calculations are made to compare the results with those by other methods, such as the geometrical theory of diffraction (GTD) and HFSS simulation. A good agreement has been observed to confirm the validity of our method.