A Hybrid technique for the analysis of pyramidal horn antennas is proposed in this paper. The transition from a relatively small feeding waveguide to a larger radiating aperture is analyzed using the mode matching technique, while the discontinuity between the horn and free space is analyzed using the method of auxiliary sources. The resulting procedure is very stable and accurate while the computational time is quite small since all the coupling integrals involved in the mode matching are evaluated analytically. I. Introduction The proposed hybrid method aims at the accurate prediction of the return loss and the radiation pattern of horn antennas. Approximate methods used in the past for the analysis of this type of antennas failed to accurately calculate the VSWR as well as the far-out sidelobes and backlobe radiation patterns. A hybrid method was proposed in [1] for the analysis of conical horn antennas, where the Mode Matching Technique (MMT) was used for the evaluation of the scattering parameters of the antenna and the method of moments for the analysis of the transition between the horn and the free space. This method, restricted to circularly symmetric structures, proved to be very accurate. Liu et al [2], proposed a similar technique for the analysis of rectangular horn antennas. In the proposed paper the horn antenna is divided into a series of waveguide sections and step junctions, which are analyzed using a closed-form MMT developed in our previous work [3]. In this manner the field within the horn as well as on its aperture can be described by the MMT. In [3] we assumed that the aperture was a perfect termination for all the incident waveguide modes. This approximation causes inaccuracies, especially in the antenna input impedance and when the aperture electrical dimensions are relatively small (in terms of wavelengths). In order to overcome this shortcome this paper aims at the characterization of the aperture discontinuity as an imperfect junction between the horn and the free space. The resulting hybrid technique can accurately and efficiently evaluate the return loss and the radiation characteristics of the antenna under investigation. This is due to the closed form representation of the coupling integrals involved in the MMT, while the key feature of the MAS is the displacement of the location of the auxiliary sources with respect to the actual boundary. This last feature provides a non-vanishing distance between sources and observation points, leading to a stable numerical code. Moreover, this procedure is applicable to any waveguide or horn geometries, but it could also be applied to other structure like the leaky waveguides.