In this study, free vibration characteristics of functionally graded (FG) blades whose material properties change through the blade thickness are inspected. Finite Element Method (FEM) is used to create blade models and to calculate natural frequencies. The blade formulations are derived for both Euler-Bernoulli and Timoshenko beams to inspect the effect of different parameters on vibration characteristics. For each beam, stiffness and mass matrices are derived from energy expressions. In the solution part, effects of several parameters, i.e. rotational speed, material properties, power law index parameter, different boundary conditions and slenderness ratio are investigated. The calculated results are compared with those in open literature and a very good agreement between them is confirmed, which reveals the correctness and accuracy of the finite element formulation developed in this study. Formulations are carried out in great detail and additionally, the results are displayed in several figures and tables, which can be a significant source of information for authors working in this area.