Abstarct: In this dissertation, thermal buckling of variable thickness conical shells is studied. The considered conical shell is made of functionally graded materials, and mechanical properties of the shell vary continuously along thickness and the axis of the shell. Third-order shear deformation theory is used to derive the displacement strain correlations and then, buckling temperature is calculated using the minimum potential energy principle and semi-analytic finite element method. Since the considered shell is axisymmetric, the conical shell is modeled using a semi-analytic finite element method with second order 5-degree of freedom 3-node isoparametric elements. Thermal loading is applied axisymmetrically and with a uniform temperature increase along the shell thickness. Clamped and simple boundary conditions are assumed. The influence of different parameters such as property distribution of functionally graded material, Semi-vertex angle, wall thickness variations and various boundary conditions on strain behavior of variable thickness conical shells is studied.