The nonlinear finite element method combined with an improved arc-length method is presented for the postbuckling analysis considering the progressive failure of composite laminated shell structures. In the improved arc-length scheme, new methods to determine the direction of load-increment and to control the arc-length are introduced. In the nonlinear finite element formulation, the updated Lagrangian description method based on the second Piola-Kirchhoff stress tensor and the Green strain tensor is used. For the finite element modeling of the composite laminated shell structures, the eight-node degenerate shell element is utilized. For the failure estimation, the maximum stress criterion is applied to the average stress in the each layer of all the finite elements. To estimate the postbuckling load-carrying capacity conservatively, the stiffness and the stress corresponding to the failure mode are set to be zero. As the numerical examples, the behaviors of graphite/epoxy composite laminated cylindrical panels under axial compression are investigated form the initial loading, through the buckling and to the final collapse. Present finite element result with consideration of stiffness degradation and stress unloading due to failure shows good agreement with experiment in the buckling stress, postbuckling compression strength, failure and deformations, The postbuckling compression strength is independent of the initial buckling stress and dominated by the bending stiffness in axial direction, In the several laminated cylindrical panels with the large values of aspect ratio, prebuckling compression failure occurred at the stress lower than the buckling stress. Postbuckling failure is severe in the most outer and inner layers distant from the mid-surface due to the bending moment effect.