Asymptotic solutions for a functionally graded material (FGM) plate are developed to elucidate stress singularities at a plate corner, using a third-order shear deformation theory. The characteristic equations are given explicitly for determining the order of stress singularity at the vertex of a corner with two radial edges having various boundary conditions. The non-homogeneous elasticity properties are present only in the characteristic equations for a corner with one of its two edges simply supported. The effects of material non-homogeneity on the stress singularities are extensively examined. The present results are very useful for developing accurate numerical solutions for an FGM plate under static or dynamic loading when the plate involves stress singularities, such as a V-notch or crack.