The multi-stability of composite shells often exhibits complex mechanical behaviors, accompanied by large deformation, strong nonlinearity and multiple equilibrium branches. We present a numerical framework for stability analysis of laminated composite shells, which is capable of efficiently computing nonlinear equilibrium paths and critical points, and effectively assessing the stability of the structure’s equilibrium. The computational framework is applied to investigate several multi-stability problems in cylindrical laminated shells. Good agreement is observed even in an “extreme” experimental case where the multi-stability is highly sensitive, and it is found that the precise approximation of the strain energy is crucial for accurate prediction of shell stability. This study is believed to provide a powerful alternative to other methods for the stability analysis and the design of advanced composite shell structures