Radiation pattern prediction analysis of elliptically polarized cavity-backed aperture antennas in a finite ground plane is carried out using a combination of the finite element method (FEM), method of moments (MoM), and geometrical theory of diffraction (GTD). The magnetic current on the cavity-backed aperture in an infinite ground plane is calculated using the combined FEM-MoM analysis. GTD is used to calculate the diffracted fields due to both soft and hard polarizations at the edges of the finite ground plane. The slope of the incident magnetic field at the diffraction points is derived and analytical expressions are presented. Numerical results for the radiation patterns of a cavity-backed coaxial cavity and also a cavity-backed circular spiral microstrip patch antenna excited by a coaxial probe in a finite rectangular ground plane are computed and compared with measured results.