Radiation of antennas under electrically large hemispherical and geodetic antenna covers is considered. The Green's functions for layered structures are used for reflection and transmission electric field calculation. The reflected and transmitted electromagnetic field is calculated as radiation of the equivalent electric and magnetic currents on the illuminated radome surface. Sandwich-type antenna radome structure is taken into account in characteristic part of Green's functions so far field is calculated very quickly. Circular polarized wave transmission through layered structure is investigated. Radiation pattern distortion occurs by the antenna radome structure and antenna location under the radome is analysed. The decrease in antenna gain, sidelobes growing, boresight errors and depolarization of aperture antennas and antenna arrays caused by radomes are analysed. The method is suitable for quick computer modelling of antenna radomes and optimization of its properties.