This paper presents new results regarding damping of structural vibrations using the elastic wedge method. An elastic wedge is a plate, or a rod, whose thickness decreases smoothly towards zero. Flexural vibration energy accumulates at the thinner edge and thus, effective damping can be easily achieved. The method has been proposed to reduce flexural vibrations of structures in the high frequency range, like vibration of turbine blades. In this research, the application of the elastic wedge method to reduce structural vibration in low frequency ranges is investigated using FEM. The structure under analysis is a heavy machinery bed structure. Two rod elastic wedges are attached to that bed. The target frequency range to be damped is between 150 and 250Hz. The results show that the elastic wedge method can effectively reduce the structural vibration of the bed in the target frequency range. Moreover, it was also found that, contrary to results previously published, for the researched structure longer and thinner elastic wedges are not the optimum option. This is an important point when considering the difficulties of manufacturing very long and thin elastic wedges.