The aim of this research is to examine the mechanical buckling behavior of multi-layered functionally graded beams in the axial direction. Numerical buckling analyses were performed using finite element software called ANSYS. Each beam configuration is suggested to be three layers prepared using various percent volume fractions of Zirconia (ZrO2) and Aluminum (Al) materials. The levels of layers and layer positions of the beams were evaluated according to Taguchi's L-9 (33) orthogonal array technique. Layers were determined as control factor and so nine numerical analyses were performed under clamped-clamped boundary conditions. The first mode shapes of the axially layered functionally graded beams were demonstrated in order to detect the most affected layers as visually. Analysis of signal-to-noise ratio was applied to obtain the optimum levels of layers. Analysis of Variance (ANOVA) was employed to solve the layers with significant impacts and their percent contributions on numerical results. The maximum buckling load was determined using various positions of layers with the optimum levels obtained based on Taguchi methodology.