New results of buckling and postbuckling analysis are presented for a shear deformable anisotropic laminated cylindrical shell of finite length subjected to torsion. 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 loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling response of perfect and imperfect, moderately thick, anisotropic laminated cylindrical shells with different values of shell parameters and stacking sequence. The postbuckling equilibrium path is unstable for a moderately thick laminated cylindrical shell under torsion and the shell structure is virtually imperfection-sensitive.