[en] The fiber-wound composite cylindrical shell has the characteristics of simple structure, high specific strength, high specific rigidity, strong design and high bearing capacity, and is widely used in pressure vessels, aviation, aerospace and military industries. At present, the cylindrical shell we use usually consists of a small angle layer and a circumferential layer, after the small angle layer is wound and formed on the core mold, it needs to be de molded into the initial test piece, and then subjected to large tension secondary winding forming, improper design is likely to cause entanglement instability problems. In this paper, the Ritz method theory is used to derive the stability equation of the small-angle layer shell, and the critical instability pressure and the prestressing force are obtained, then the initial test piece lay-up structure is given in combination with the actual winding process, and the material parameters and cylindrical shell are also carried out, the influence of wall thickness factors on critical instability pressure. This study provides theoretical support for the rational design of fiber-wound composite cylindrical shells. (authors)