This paper analyses results of buckling analysis of functionally graded (FG) beams, HSS-sections and I-sections using the Reyleig-Ritz method. Buckling analysis is made for two types of supports: section simply-suported from both sides and section clamped on one side and simply-suported on the other. The Reyleigh-Ritz method is a method based on the variational formulation of the problem. The variational formulation is based on a functional. From stationarity conditions of the functional it is possible to derive a differential formulation. That is, condition of stationarity containes differential equations and corresponding boundary conditions. In order to obtain a solution, it is necessary to satisfy the stationarity condition of the functional describing the problem. Functionally graded (FG) materials are a type of two component composite materials that have a continuous property change of material from one surface to another. The components of a FG material are usually ceramics and metal. The FG materials at the boundaries contain pure components of the composite, which enables the full usage of their properties. Using the tables and graphically presented results in this paper, it is possible to obtain results of buckling analysis for different dimensions of sections.