In this paper, buckling analysis of functionally graded super-elliptical plates is investigated by pb-2 Ritz method. The governing equation is derived based on classical plate theory (CLP). Since closed form solution of buckling differential equation is not available under various boundary conditions, pb-2 Ritz method (energy method) is applied to calculate non-dimensional buckling load. Total potential energy is given as summation of strain energy and work done by applied in-plane compression load. In order to obtain the buckling load, pb-2 Ritz method is applied corresponding to different peripheral supports (Clamped and Simply Supported) are used in the present study. The plates are assumed to have isotropic, two-constituent material distribution through the thickness and the modulus of elasticity of the plate is assumed to vary according to a power-law distribution in terms of the volume fractions of the constituents. Variation of buckling non-dimensional parameter is considered with respect to various powers of super–elliptic, FGM power law index and aspect ratio.