In this thesis, a computationally efficient model is proposed to determine different performance parameters of a conical horn antenna of arbitrary profile numerically over a wide range of frequencies. The model is developed using mode matching technique that solves the waveguide junction problem and an integral equation technique that solves the waveguide aperture free-space transition. It has functions to evaluate the S parameters, near-fields and far-fields of the antenna. Rigorous testing of the proposed novel technique has been done using MATLAB and the results have been verified by comparing them with the results obtained from commercial tools like FEKO and CST. This technique is capable of finding the performance parameters of the antennas faster than the available solvers in commercial tools like FEKO and CST. Furthermore, various goal functions are proposed for the optimization of some of the performance parameters such as the S parameters, the cross-polarization levels, and the aperture efficiency. These goal functions can be used to find optimum horn antenna feed profiles for radio astronomy applications.