A polynomial series expansion for displacements is used in conjunction with the Rayleigh-Ritz energy method to produce buckling and post-buckling stress solutions for an elliptically-shaped surface layer that has been delaminated from the main load-bearing body. Plate deformations are induced by a combined in-plane displacement field applied to the plate boundary and normal pressure. Convergence of the plate solution is assessed by systematically increasing the number ofdisplacement terms in the series expansion. The convergence of membrane and bending stresses at the plate boundary was generally slow and nonuniform. The degrees-offreedom necessaryfor a satisfactory solution typically increase with increasingcomplexity or magnitude of the plate deformations. By employing as many as 77 displacement terms, practically exact stress solutions are obtained for a wide variety of basic delamination plate problems. The proposed solution procedure is highly efficient and economical, and it may be easily extended to other plate geometries or loading conditions.