Modeling of elastic boundary support is crucial for simulating realistic vibro-acoustical behaviors of plate-like structures. In this paper, the mechanical and moment impedances of an elastic support material are derived in closed form under several assumptions, and three basic studies are conducted on a vibration system of a thin plate supported with an elastic material. First, bending wave reflection from the impedance boundary is theoretically analyzed to clarify the incidence angle dependence of vibration energy absorption coefficient. Second, the proposed impedance model is validated in comparison with the precise finite element model of the elastic support material. Finally, as an application of the impedance model, loss factor measurement is numerically modeled, which reveals that the calculated loss factors are generally greater than the theoretical values for the diffuse vibration field.