Development of higher-order shear deformation theories remains one of the principal areas of mechanics of composite materials. An outline of the work done in this direction for composite plates was presented by Noor and Burton [l]. Higher-order theories for composite shells were considered by Reddy [2], Librescu [3], Dennis and Palazotto [4], etc.

Governing equations of higher-order shell theories are very complicated. This explains a small number of closed-form solutions that have been published. Mentioned here are the papers published by Reddy and Liu (51 and Barbero, Reddy and Teply [6] where Navier-type solutions were obtained for bending problems and natural frequencies of simply supported shells. Obviously, solutions for arbitrary boundary conditions have to be obtained numerically.