A finite element program using degenerated shell element was developed to solve the geometric, material and combined nonlinear behaviors of composite laminated shell. The total Lagrangian method was implemented for geometric nonlinear analysis. The material nonlinear behavior was analyzed by considering the matrix degradation due to the progressive failure in the matrix and matrix-fiber interface after initial failure. The result of the geometric nonlinear analysis showed good agreement with the other exact and numerical solutions. The results of the combined analyses considered both geometric and material nonlinear analyses were compared with the experiments in which internal pressure was applied to the filament wound antisymmetric tubes.