This paper aims to present the convergence behavior of triangular elements in buckling analysis under the mechanical and thermal load of square FGM plate problems. FGM is a new composite material with high-temperature and structural flexibility resistance. This material generally consists of ceramic and metal composition where the material properties change proportionally across the thickness. As a composite material, FGM is one of the most popular green materials used in many applications for high-temperature environments. It is essential to evaluate this material's critical buckling load or critical buckling temperature. For the performance of this material in buckling analysis, a numerical evaluation can be used to find the critical load or critical temperature. Three triangular elements (DKMT, DST, and MITC3) have been used in the study. These three elements give convergence results in static and free vibration analysis. For the buckling analysis, the results show that the three elements give good results in square FGM plate problems. The DKMT element shows superior results compared to the others. This phenomenon is due to the quadratic interpolation used in the DKMT element. © 2024 Author(s).