Abstract: In this paper, the analytical solutions of the steady-state responses of a viscoelastic rod in Kelvin’s model subjected to time-harmonic forces are derived based on Green’s function method and the superposition principle. Laplace transform method is employed to obtain Green’s function for the forced vibration of the viscoelastic rod with arbitrary boundary conditions. A unified strategy applied to various boundaries is proposed to determine unknown constants involved in the Green’s function. Computational results show that the dynamic deflection of the rod considering viscous damping of the material and external damping is not separable in time and space.