We have derived the novel extended UTD (Uniform Geometrical Theory of Diffraction) solution and the novel modified UTD solution for the back scattering of an incident whispering gallery (WG) mode on the edge of a cylindrically curved conducting sheet. By comparing with the reference solution obtained from the integral representation of the scattered field by integrating numerically along the integration path, we have confirmed the validity and the utility of the novel asymptotic solutions proposed in the present study. It is shown that the extended UTD solution can be connected smoothly to the modified UTD solution on the geometrical boundary separating the edge-diffracted ray and the surface-diffracted ray.