A high-frequency solution for the diffraction from a strip with two arbitrary face impedances, illuminated at edge-on incidence, is obtained by a spectral extension of the geometrical theory of diffraction. An asymptotic approximation of the solution given by Maliuzhinets for the half plane is used. Uniform expressions for the scattered far field are given for cylindrical and plane wave illuminations. Incidence perpendicular to the edges of the strip is considered in both TE and TM cases. In the case of plane wave illumination the expressions for the field are greatly simplified. Numerical results are presented. In particular for resistive strips, the backscattered field calculated from this solution compares very well with that calculated by other techniques.