The bi-stable composite materials can be widely used in the design of variable structures. Using ABAQUS/Standard(version 2018), a finite element analysis of the shell′s snapping process was conducted to simulate the snap-through process and snap-back process of the bi-stable cylindrical shells with anti-symmetric laminated carbon fiber composites. The distribution and trend of the stress on the cylindrical shell during the whole continuous process were discussed to give advice to the design of this type of variable structure. The results show that the stress distribution of the composite cylindrical shells is very different during the snap-through process, the snap-back process and the second stable state. Moreover, the maximum stress moment on the entire cylindrical shell does not overlap with the moment when the maximum load is applied, and has hysteresis.