In this study, free vibration analysis of a functionally graded (FG) beam under various boundary conditions is carried out. Natural frequencies of the FG beam are analysed by using Finite Elements method. The system of equations of motion is derived by using Lagrange's equations with the assumption of Euler Bernoulli beam theory. The material properties of the beam are assumed to vary through thickness according to power-law form. Different boundary conditions are attained by applying different stiffness values to the springs connected at the ends. The model is validated by comparing the results with previous studies. The effects of various material distributions and spring support values on the natural frequency parameters of the FG beam are discussed in detail.