State-of-the-art radomes exploit frequency selective media so as to be transparent for the frequencies of the antenna protected by them and opaque to other frequencies. This feature helps in reducing the radar cross section of the antenna and in protecting it from interference. The study of a frequency selective radome is a daunting task, since the radome is usually large in terms of wavelengths, hence full wave analyses are prohibitive. In this paper an approximate technique, based on the physical optics concept, is proposed to attain an estimation of the behavior of a radome shielded antenna in a short time with a commonly available computer. Results are validated against a full wave technique over a relatively small radome.