An asymptotic Green's function technique is presented for the calculation of the surface fields on a perfect electric conductor circular cylinder covered with a dielectric layer. The sources are apertures located on the perfect electric conductor surface. This method is very efficient and valid for large cylinders in terms of wavelengths. The new representation is obtained via Watson's transformation and integral contour deformations. The efficiency of the method results from the circumferentially propagating representation of the Green's function as well as the efficient numerical evaluation of various integrals. Numerical results are presented showing good agreement when compared to other solutions as well as measurements.