The effects of both anisotropy in the substrates and the superconducting films on the resonant frequencies and radiation patterns of an equilateral triangular patch are investigated theoretically. Our proposed method is based on the modified cavity model in conjunction with the electromagnetic knowledge. The validity of the proposed method is tested by comparing the computed results of the resonant characteristics with experimental data. Results show effects of the superconducting patch thickness as well as the anisotropy in the substrate on the resonant frequency and the radiation pattern of the triangular patch. The effects of the antenna parameters on resonant frequencies and radiation patterns are also presented and discussed. At higher substrate thicknesses, numerical results indicate that the radiation pattern is drastically changed. The resonant frequency, on the other hand, decreases with high equivalent permittivity of the anisotropic substrate. The proposed method is very fast, simple, and compatible well with CAD.