Abstract: On the basis of Ref [1, 2] in this paper, we investigate the nonlinear elastic buckline problem of orthotropic laminated cylindrical panels under the action of axial load.The nonlinear constitutme relations of more ana matrix are considered. Cross-plied and ±θ angle-plied cases are discussed. The small elastic-plastic deformation theory and the law of mixture of tomposite materials and the linear theory of stability are used. The formulas for the critical loads of nonlinear elastic buckling are obtained.The method of determining the constants of material Property from some simple experiments.Numerical examples and discussions are given. The experimental methods to measure the nonlinear elastic constants of unidirectional composite lamina are given in the appendix. Only the theoretical research is done in phis paper.It is a regret that we have not suitable condition to do experimental work. But the method given in this paper is valuable to the engineers and researchers.