The application of Viscoelastic (VE) supports in order to dampening dynamic forces and energy dissipation has been investigated herein. Properties of viscoelastic substances are important in the quality and quantity of the dissipation. The viscoelastic materials were described using the generalized Kelvin-Voigt mechanical model and the resulting governing equations were solved using the finite element method in time domain. To investigate the effects of the viscoelastic characteristics of supprots on axial vibration, dynamic and quasi-steady analysis of a rod subject to axial step excitations was carried out. Finally, some important criteria were presented to improve the performance of these substances in energy dissipation. In addition, axial vibration of an elastic and a viscoelastic rod with end and middle VE supports subject to harmonic excitations were investigated. It reveals that the use of VE supports considerably damps out structural vibrations, especially at low frequencies. Whereas in high frequencies, the amount of the energy dissipation depends on the retardation times of the Kelvin-Voigt elements.