A theoretical and numerical analysis of square Van Atta reflectors has been carried out with or without a conducting plate, used for mounting of the antenna elements. The Van Atta reflector investigated has antenna elements which are parallel half-wave dipoles interconnected in pairs by transmission lines of equal electrical length. The dipoles are placed in a plane which is parallel to the conducting plate when this is present. In the theory, each pair of antenna elements with the interconnecting transmission line is represented by an equivalent circuit. The mutual impedance between the antenna elements and the reradiation from the elements as well as from the conducting plate have been taken into account. The influence of the conducting plate on the induced dipole currents has been treated using the theory of images. The scattering cross section of Van Atta reflectors with or without a conducting plate has been examined numerically using an electronic computer, and some of the results have been compared with experimental results obtained by others.