A high frequency approximation method is proposed to obtain the scattering from rectangular dielectric cuboids. Our formulation is based on a Kirchhoff type aperture integration of the equivalent current sources over the surface of the scattering bodies. The derived formulae have been used to get the radar cross section of cuboids, and the results are compared with those by other methods, such as physical optics, geometrical theory of diffraction, the HFSS simulation and measurements. Good agreement has been observed to confirm the validity of our method.