This research aims to present an overview for better understanding of bending of beams and buckling of columns of variable cross sections made of functionally graded materials (FGM). Two goals were achieved in this study, the first goal was showing the importance of using the actual position of the neutral axis instead of assuming it being at the middle of the cross section for functionally graded beams, this was achieved by modifying the strain equation To get the actual position of the neutral axis, and making a comparison for the stress, strain, axial force, axial displacement, and deflection resulted from using each case of neutral axis position. To study this effect, different functions for the functionally graded beams used; power law and exponential function with different materials combination and different values of k, different boundary conditions used; simply supported and cantilever beams. The conclusion shows how important is to use the actual position of the neutral axis. Another goal of this research is to show the value of FGM beams and columns by analyzing these elements and comparing them with different types of isotropic elements. The importance of the comparison, besides showing the importance of the FG elements, is to validate the answers. The analysis of bending and buckling of these problems using analytical method based on Euler-Bernoulli theories, FGM is considered in the transversal and axial direction of both beams and columns, different materials and different power values to consider different material concentrations were used, multiple support types used (simply supported and fixed-fixed). The comparison got in multiple stages; the first stage of comparison was between FG element (with different material concentration) and isotropic one (constant cross section), the second stage was between different materials FG elements, the third one was between FG element with variable cross section made from isotropic material, all these comparison shows the importance and value add from the concept of FG, the fourth comparison was between FG elements on X direction and FG elements on Z direction. The results show the big benefit from using FG concept in structural elements, especially FG in the X direction.