A hybrid method consisting of employing the mode matching method in conjunction with the Fourier transform technique is used to analyze the radiation of the lowest order TM-wave from an impedance loaded parallel plate waveguide. In contrast to the classical formulations which lead to an intractable matrix Wiener-Hopf equation, the hybrid method that we will adopt reduces the related boundary value problem into a scalar modified Wiener-Hopf equation of the second kind and bypasses the most challenging step of matrix Wiener-Hopf factorization. The solution involves infinitely many unknown constants satisfying an infinite system of linear algebraic equations which can be solved approximately through numerical procedures. Some computational results showing the effects of the impedances of the plates and the plate to plate separation distance on the radiation phenomenon are also presented.