Abstract: In this paper,stability of multi-layer composite circular cylindrical shells un-der axial compression is systematically dealt with.Based on Donnell equations,the method of displacement is extended to this problem.With the consideration of eight different boundary conditions,theoretical solutions for prebuckling,buckling mode and calculation of critical load are presented here.The emphases are placed on boundary conditions and coupling effect.The theory and results can be directly applied in the structural design of shells of rocket engine.