This paper deals with dynamic analysis of functionally graded beams on elastic foundation considering damping effect. It is assumed that the mechanical properties of the material vary along the beam thickness. The fourth-order differential equation is analytically solved by means Green\\\'s function method, and exact answer is achieved. Damping effect, which is an intrinsic property of structures with great influence on the forced vibration of mechanical systems is included in the analysis. However, due to difficulty involved, it is usually neglected in the analysis of structures. Furthermore, the effect of rotary inertia is considered in the problem formulations. Green’s function method is a straightforward way to model physical problems subjected to arbitrary loads and affected by various parameters, such as, elastic foundation, damping, geometry and mechanical properties. It could be a unique solution to gain the exact answers via the superposition manner. To demonstrate the accuracy and efficiency of the presented solution, dynamic response of the beam under different harmonic loads is obtained and compared to available results in some cases.

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