Flexural waves traveling in an elastic wedge (plate whose thickness decreases towards zero following a power law function) are not reflected back and accumulate at the zero thickness edge what results in a very efficient damping. In practice reflection always occurs because manufacturing a zero thickness edge is not possible. To solve that problem Krylov proposed the addition of a small quantity of damping material on the thinner edge of the plate what results in very effective damping. In this paper, the application of elastic wedges to reduce the vibrations of turbine blades is investigated. The objectives of this research are to evaluate the damping effectiveness of elastic wedge theory in blades and second, to evaluate a non-polymeric material as vibration damping material. In this way, the vibration energy of the blade is dissipated by the damping material and, at the same time, high temperature and low strength problems characteristic of polymeric damping materials are prevented. First, a FEM modal analysis of a simplified blade model is performed to understand the effects that the elastic wedge has on the modal shapes and frequencies of the blade. Next, to evaluate the damping levels achieved, a frequency response of the simplified blade model with and without elastic wedge is evaluated with the added damping material. The results show that elastic wedge theory combined non-polymeric damping materials can be an efficient method to reduce vibrations of turbine blades or similar applications.