A rigorous radar cross section (RCS) analysis is carried out for two-dimensional rectangular and circular cavities with double-layer material loading by means of the Wiener-Hopf (WH) technique and the Riemann-Hilbert problem (RHP) technique, respectively. Both E and H polarizations are treated. The WH solution for the rectangular cavity and the RHP solution for the circular cavity involve numerical inversion of matrix equations. Since both methods take into account the edge condition explicitly, the convergence of the WH and RHP solutions is rapid and the final results are valid over a broad frequency range. Illustrative numerical examples on the monostatic and bistatic RCS are presented for various physical parameters and the far field scattering characteristics are discussed in detail. It is shown that the double-layer lossy meterial loading inside the cavities leads to the significant RCS reduction.