This paper analyses results of buckling analysis of functionally graded (FG) beams, HSSsections and I-sections using Galerkin’s method. Functionally graded materials are two component composite materials (usually metal and ceramic) with a continual property change in between the faces of the material. Functionally graded materials have pure forms of both of their components on the edges of the material. Differing from functionally graded materials, two component composites that are a homogenous mixture of the two components cannot fully utilize properties of either of the components. Instead we get a material with properties that are a compromise between the properties of the two components. To solve differential equations describing buckling of different FG sections we use Galerkin’s method. Galerkin’s method belongs to a group of numerical methods called “meshless” numerical methods. Meshless because the discretization of the observed area is conducted on the nodes with dependent variables. Numerical methods allow for a simple and fast change of the input parameters and the solution of the problem. We analyze how the change of input parameters affects the output values. Comparing results calculated by numerical methods with results calculated by analytical methods we can evaluate the accuracy of the numerical method. Results of critical buckling loads using different input parameters are shown tabulated and graphically.