A boundary layer theory for buckling and postbuckling of anisotropic laminated thin shells is extended to shear deformable stiffened anisotropic laminated shells. A postbuckling behavior is investigated for a shear deformable anisotropic laminated cylindrical shell with geodesical stiffener of finite length subjected to lateral or hydrostatic pressure. The material of each layer of the shell is assumed to be linearly elastic, anisotropic, and fiber-reinforced. The governing equations are based on a higher-order shear deformation shell theory with von Kármán–Donnell-type of kinematic nonlinearity and including the extension/twist, extension/flexural, and flexural/twist couplings. The nonlinear prebuckling deformations and initial geometric imperfections of the shell are both taken into account. A singular perturbation technique is employed to determine the buckling pressure and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling response of perfect and imperfect, moderately thick, geodesically stiffened shells, axial and ring stiffened shells, and unstiffened shells with different values of shell parameters and stacking sequence. The results confirm that there exists a circumferential stress along with an associate shear stress when the shell is subjected to lateral pressure. The postbuckling equilibrium path is stable for the moderately long shell under external pressure and the shell structure is virtually imperfection-insensitive.