Abstract: The non-axisymmetric buckling and post-buckling of a polar orthotropic annular plate whose edges are clamped and its outer edge w subjected to a uniform radial compres-sive force is analysed by using a shooting method. Eigenvalues are calculated and the existence of bifurcation solutions is discussed. The asymptotic fomulse of the bifurcation solutions are obtained aad the buckling behaviour of the annular plate is analysed.