Radiation from a two dimensional reflector antenna covered by a cylindrical radome is analyzed by the complex dual series approach. It is only performed for the electrically polarized incident field. The approach is based on the analytical numerical type regularization technique and not on the moment method. This method gives the exact solution with any desired accuracy and the directivity of the feed antenna can be modelled by using this method. The results can be thought as a reliable data for the validity of approximate solutions. The lossy case and the multilayer radome problems can be solved by the same method.