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• An isogeometric method for buckling analysis of composite cylindrical shells under external pressure is proposed. • Based on Reissner–Mindlin shell theory, effects of large deformation is considered in this method, and a modified arc-length method is proposed to track the equilibrium path after limit points. • Post-buckling analysis of different composite pressure shell models are computed and verified, both snap-instability behavior and bifurcation behavior are observed. • For linear buckling analysis of variable stiffness composite shell cases, the efficiency of the proposed method is confirmed for achieving same precision as FEM with fewer elements. Composite cylindrical pressure hulls are thin-walled structures widely used for autonomous underwater vehicles. Buckling failure is one of the most important failure modes for these shells under external pressure. In existing buckling studies of cylindrical pressure hulls, FEM is the most popular analysis method but not efficient enough when dealing with structures with complex material distributions such as the variable stiffness composite shells. Motivated by this, an isogeometric method for buckling prediction and post-buckling analysis of variable stiffness composite underwater pressure shell is proposed in this article. In this method, based on Reissner–Mindlin shell formulas undergoing large deformation, a buckling analysis framework in IGA forms is established. Then a modified arc-length method is proposed based on kinematics used in the shell formulas, and is used to overcome the inaccuracy caused by the 2 degrees of freedom node rotation in the prediction step of arc-length method. In addition, the influence of bifurcation is considered, which may seriously affect the precision of buckling behavior simulation when the limit point is close to a bifurcation point. The computational accuracy of this framework has been validated in a series of constant stiffness composite shell cases involving buckling load prediction and post-buckling behavior simulation. For variable stiffness composite hull cases, this framework achieves the same precision as FEM with fewer elements. Therefore, the proposed framework provides an efficient way for the buckling design of underwater variable stiffness composite pressure hulls. [ABSTRACT FROM AUTHOR]