In order to analyze the influence of the hyper-damping isolator on the dynamic characteristics of elastic beam, the dynamic mechanical models of the beam on single-layer and two-layer continuous elastic foundation were presented, respectively. The dynamic responses of the elastic beam under harmonic steady excitation were given in space-frequency domain. For comparison, the definition of force transmission ratio and vibration decay rate along the vertical and horizontal direction of the elastic beam were provided, respectively. Then, the control effectiveness of the hyper-damping isolator on the dynamic characteristics of the beam on the elastic foundation was evaluated. The calculating results show that the amplitude of the transmission force rate and decay rate of the flexural wave in space domain can be enhanced by using the hyper-damping isolator when compared with the common linear elastic foundation. Besides, the system frequency of the beam with hyper-damping isolator was higher than the beam on elastic foundation. Finally, the effective working frequency range, the amplitude of the transmission force rate and the vibration decay rate of the beam can be optimized by adjusting the parameters of stiffness ratio ε and the safe coefficient α of the hyper-damping isolator.