The Rayleigh-Ritz method has been used to analyse the buckling and pos
tbuckling behaviour of thin elliptical anisotropic plates. Different l
ayups and ellipse orientations were analysed and compared with finite
element results showing good agreement in displacements and total ener
gies in the postbuckled regime. The energy release rates along the hal
f axes which govern the onset of unstable delamination growth were com
puted for strains up to the third buckling mode.