In this paper, elastic stability of polar orthotropic annular plates subjected to in-plane uniform radial edge pressures has been considered. The Rayleigh-Ritz method with simple polynomials as admissible functions has been employed in the analysis. It has been established that spectra of eigenvalues for axisymmetric buckling are identical for free-free, simply supported-free, and free-simply supported combinations of edge conditions. For a hole ratio of 1/2, numerical estimates to the least axisymmetric buckling loads have been obtained for all combinations of free, simply supported, and clamped boundary conditions for two loading cases, namely: (1) when the outer edge alone is subjected to uniform presure, and (2) when both edges are subjected to equal pressures. Some interesting effects of the rigidity ratio on these buckling loads have been brought out.