Abstract: Based on an accurate mathematical model of the post-buckling of axially extensible rods, a numerical analysis of the post-buckling behavior of simply supported compressed FGM rods by a shooting method is presented in this paper. In the analysis, it was assumed that the material properties of the rods vary continuously as a power function of the thickness coordinate. The post-buckling characteristics curves of FGM rods under the different graded index are plotted, which are compared with the those of pure metal and ceramic material columns. The effects of the load, material gradient property and slender on the buckling deformation of beam are discussed in details.