The full-wave spectral domain technique is used for the first time to analyse the single and covered triangular patch antennas fed by the coaxial probe. The equilateral triangular patch antenna fed by a probe along the patch median was analysed and its input impedance and radiation patterns are presented. The effects of flat radomes on these parameters are studied. To avoid excessive computation time, three sets of basis functions representing the approximate current distributions on the patch are introduced. Merits of each set of basis functions are discussed. Various tests were made to establish the validity of the basis functions, including comparisons of the results against those obtained by the cavity model and against those of some experimental observations.