This chapter deals with mechanical and thermal buckling of plates, which are functionally graded with two-constituent materials through the plate thickness. A power-law variation is used for the material variation. The third-order theory of Reddy (1984) is used with thickness stretch to formulate the equations governing buckling. A displacement finite element model with seven degrees of freedom (3 midplane displacements, three rotations, and a stretch) is developed. Numerical results of buckling loads and critical temperatures are presented and compared with results available in the literature. The present model is found to be accurate and robust, without experiencing locking, which is a major issue with existing finite element models.