We study the refraction of a plane electromagnetic wave on a two dimensional array of rf-SQUIDs. The basic equations describing the amplitudes of the magnetic field and current in the split-ring resonators are derived. The reflection and transmission coefficients analyzed annalistically in the linear approximation. We show that the polarization of the reflected wave is independent of the frequency of the incident wave and of its polarization; it is defined only by the orientation of the split ring (analog of Kerr?s effect). Polarization of the transmitted wave depends both on the frequency of the incident field and orientation of rf-SQUID (analog of Faraday?s effect). The reflection and transmission coefficients have a resonance that is determined by the parameters of the rf-SQUID; its strength depends essentially on the angle of incidence. At the higher intensities of the incident field nonlinear response of rf-SQUID leads to bistability of field refraction. We studied properties of this bistability and evaluated its characteristic parameters.