A rigorous formulation is suggested for solving the scattering of plane waves by a composite wedge of metal and lossless dielectric. This employs the Kirchhoff integral in the physical regions and the extinction theorem in their mathematical complementary regions to make the correction of the primary approximated solutions. Calculated total field patterns scattered by the composite wedge give close results to the rigorous asymptotic field for the limits of the dielectric wedge becoming conducting or background free space. (C) 1997 John Wiley & Sons, Inc.