Localized buckling of anisotropic shells is studied in this paper. Elastici
ty relations for a shell consisting of the matrix reinforced by fibers are
obtained for the general anisotropic case. Equilibrium equations are simpli
fied by considering the assumptions usually made for the Donnell theory. Fo
r one parametric loading: the critical pressure and the buckling modes are
obtained by means of the asymptotic method.