Bistable composite structures have a wide application prospect in the design of deformable structures. In this study, the snap behaviors of unsymmetric cross-ply bistable composites with different thicknesses are investigated. Besides the experiments, the relationships between load and displacement during the snap process are also analyzed by finite element (FE) methods. The load-displacement curves of composite shell with four layers and two layers are completely different. The results of the two-layer cylindrical shell with resin layer are in good agreement with the experimental results. The resin layer has great influence on the snap behaviors of the two-layer bistable cylindrical shell, although it has little effect on the four-layer cylindrical shell. So it cannot be ignored in the analyzing of two-layer bistable shell. The cause of experimental errors is also analyzed. The research results of this paper have reference value for the engineering design of bistable composite structures.