In the present article, the critical buckling temperature of axially layered functionally graded thin beams for the first mode was studied under clamped-clamped boundary conditions. The beams were made to be three layers using functionally graded materials with ceramic and metal systems in the axial direction. Analyses were performed using fmite element and Taguchi methods. The beam configurations were designed based on Taguchi L-9 orthogonal array in order to detect the maximum critical buckling temperature and were analyzed using finite element software ANSYS. Analysis of signal-to-noise ratio was utilized to determine the layers with optimum levels and the influence of ceramic and metal materials in each layer. Analysis of Variance at the 95 % confidence level was employed in order to select the most significant layers and their percent contribution on response characteristic. The optimum result of the critical buckling temperature was predicted based on the 95 % confidence intervals of confirmation analysis and population.