本文以三維彈性力學理論為基礎，不對位移或應力預作假設，根據微小擾動法來推導異向性且非均質複合圓柱層殼，在分別受軸力與扭力作用挫屈之漸近解析理論。文中將三維彈性力學之控制方程式，藉由一個適當微小參數，利用漸近展開法，分解成不同階數之控制方程式；再將各階方程式沿厚度方向依序積分，推導得各階位移與應力之二維控制方程式。根據最低階位移與應力之二維控制方程式，求出滿足於軸力與扭力作用下邊界條件之解析解；再利用最低階之解析解，求取高階之解析解；使低階至高階的解析解具有遞迴的特性。根據本文推導所得的解析解，發現在簡支承的邊界條件下，受軸力或扭力作用挫屈之數值範例結果，在與其他文獻比較下，其精度與收斂性均可達理想之預期結果。

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