An asymptotic high frequency solution is presented for the problem of electromagnetic wave diffraction by an open-ended parallel plate waveguide cavity with impedance walls, using the Wiener-Hopf techniques. By using the 'image bisection principle' the original problem is converted into two simpler ones. By expanding the total field in the waveguide region into a series of normal modes and using the Fourier transform techniques elsewhere, one obtains a modified Wiener-Hopf equations (MWHE) of the third kind for each excitations. The solution of these MWHE can explicitly be obtained by solving infinite number of constants satisfying an infinite system of linear algebraic equations. Representative numerical examples, illustrating the