A higher-order shear deformation theory is developed for accurately ev
aluating the transverse shear effects in delamination buckling and pos
tbuckling of cylindrical shells under axial compression. The theory as
sures an accurate description of displacement field and the satisfacti
on of stress-free boundary conditions for the delamination problem. Th
e governing differential equations of the present theory are obtained
by applying the principle of virtual displacement. The Rayleigh-Ritz m
ethod is used to solve both linear and nonlinear equations by assuming
a double trigonometric series for the displacements. Both linearized
buckling analysis and nonlinear postbuckling analysis are performed fo
r axially compressed cylindrical shells with clamped ends. Comparisons
made with the classical laminate theory and a first-order theory show
significant deviations.