In the present work a study on the analysis of free vibration in functional graded beams is presented, to find the natural frequencies in the beams using an improved first order theory. Five fundamental variables are considered for the field of displacements and the Hamilton Principle is used in the Finite Element Method. The first isotropic beam vibration values are calculated for different length and thickness ratios. The results obtained are compared with other studies in the literature to compare the accuracy of the method.