This paper presents a finite element method (FEM) free and forced lateral vibration analysis of beams made of functionally graded materials (FGMs). The temperature dependency of material properties along with damping had not previously been taken into account in vibration analysis. In the present study, the material properties were assumed to be temperature-dependent, and were graded in the thickness direction according to a simple power law distribution of the volume fractions of the constituents. The natural frequencies were obtained for functionally graded (FG) beams with various boundary conditions. First, an FG beam was assumed to be isotropic (metal rich) and the results were compared with the analytical solution and the results for ANSYS and NASTRAN software. Finally, dynamic responses were obtained for damped and un-damped systems. Numerical results were obtained to show the influences of the temperature dependency of the materials properties, the boundary conditions, the volume fraction distribution (the index of power law, N) and the geometrical parameters.