Based on the Timoshenko-Mindlin kinematic hypothesis, the Donnell-type shell theory is extended to include transverse shear and rotary inertia for the nonlinear analysis of an anti-symmetrically laminated cross-ply circular cylindrical shell. The resulting governing equations are expressed in terms of a stress function, two rotations and transverse displacement. The shell is assumed to be all-simply-supported and all-clamped. A solution is formulated by a multi-mode approach and the method of harmonic balance for nonlinear vibrations. The corresponding postbuckling problem is treated as a special case. The results are compared with available data. © 1988.