The corrugated conical horn with elliptical cross section is investigated. Use is made of the analytical solutions of the Lamé differential equations. In the investigations we use the anisotropic surface impedance model. The problem of wave propagation in an anisotropic elliptical cone is formulated as an eigenvalue problem. This problem is solved, and plots are given of the separation constant as a function of the opening angle of the cone with the aspect ratio of the elliptical cross section as a parameter. The radiation of an anisotropic elliptical horn excited by a hybrid mode is determined using the spheroconal wave expansion method. Satisfactory agreement between computations and measurements is obtained. It is found that with this type of horn it is theoretically possible to perfectly generate circularly polarized radiation patterns of elliptical cross section.