In this paper, buckling analysis of thick cylindrical shells using the third order shear deformation theory is carried out. The governing differential stability equations are obtained based on the second Piola-Kirchhoff tensor and are integrated across the thickness of the shell. These equations are developed in terms of components of the displacement field using third order shear deformation theory and solved analytically. It is assumed that material properties of the shell vary smoothly through the thickness according to a power law distribution of the volume fraction of constituent materials, while the Poissonâs ratio is assumed to be constant. Also governing equations are discretized and reduced to a linear system of homogenous equations using differential quadrature method. The results obtained by the present work are compared with finite element solutions and results reported in the literature and the accuracy of this method is shown. Effects of various parameters including the boundary conditions, volume fraction, different loading conditions and geometric ratios on the buckling behavior of functionally graded thick cylindrical shells are investigated.