Abstract: The generalized Donnell type equations governing large deflection of antisymmetrically laminated cross ply cylindrical shells counting for transverse shear deformation are presented. An asymptotic series solution is constructed by the perturbation technique of deflection type for buckling and postbuckling behaviors of the cylindrical shells under external pressure. Boundary layer effects at both ends of shells are considered and, for consistancy of the boundary value problem, the boundary layer solutions are also designed to match the out of plane boundary conditions by the singular perturbation approach. Meanwhile, effects of transverse shear deformation, Batdorf parameter, modulus ratio and initial geometrical imperfection on the buckling and postbuckling of the shells are examined. Numerical results computed from the present solution present the buckling loads and postbuckling equilibrium paths of the specific cylindrical shells under external pressure. It has been shown by the present solution that the decrease in buckling loads due to transverse shears is significant.