Abstarct: In this thesis, mechanical and thermal buckling have been studied separately and in the form of thermomechanical buckling of perforated plates with sector geometry made of functionally graded material (FGM). Mechanical loading conditions are of uniform compressive type in radial, circumferential and/or biaxial direction and thermal loading is affecting the whole sector by uniform temperature increase. FGM sector is considered to be from basic surfaces of zirconia and aluminum which properties changes non-symmetrically and gradually from one surface to another and it follows power law relation. The direction of properties change is considered in all three main directions, unlike most conducted researches, so that the effect direction of properties changes on the buckling load will be clarified. Existence of one or two circular hole in sector(s), has added to the complexity of the analysis. Methodology of the analysis in this thesis is finite element method baxsed on energy and 3D elasticity theory which using Trefftz stability conditions (resetting first and second potential energy to zero). Unlike most researches, a rectangular cube 3D 8-noded element is considered in finite element method which has elements in the direction of thickness. From relations of green non-linear strain-displacement for geometric stiffness matrix is used. Next, the effect of various parameters such as sector dimensions, cut-out presence and dimensions, mechanical loading direction, boundary condition, direction and power law index of graded material on the load leading to buckling is investigated.