Abstract: The buckling and post-buckling behaviors of a functionally graded material(FGM) column under distributed load were analysed. Based on the large deformation theory and consideration of the axial extension of the column, the quilibrium equations with geometric nonlinearity of an elastic FGM column subjected to distributed load were established. In the analysis, it was assumed that the material properties of the column vary continuously as a power function of the thickness coordinate. By using shooting method and analytical continuation, the nonlinear boundary-value problem was solved numerically and buckling and post-buckling response of FGM column with free- fixed edges were obtained. The post-buckling characteristics curves of FGM column under the different graded index were plotted, which were compared with the those of pure metal and ceramic material columns. The effects of material gradient property on the buckling deformation and critical load of beam were discussed in details.The results show that the post-buckling behavior of the FGM column are different from that of homogenous column, and the gradient index of the material have significant effect on the bucking load and post-buckling behavior of the FGM columns.