The most problematic eigenmode in machines involving flexure mechanisms is represented by flexural modes. However, it can be noticed that also out-of-plane modes, that occur in the space outside the nominal plane of movement of the mechanism, can be very important, especially in machines with several and coupled degrees of freedom, like 3D positioning stages. In this thesis a new design based on piezoelectric shunt damping is proposed in order to tackle out-of-plane modes of flexure mechanisms, without affecting the capability of attenuating the more common flexural modes. This new concept is validated both analytically and using the FEM software COMSOL and it is shown that attenuations of the order of 15 dB can be achieved. Furthermore, the possibility to add active control to the shunted piezoelectric materials, giving rise to a hybrid control strategy, is explored and it is shown that it results in further increase of the added damping. Finally, a completely new technique based on Eddy current dampers is discussed and shown to be inadequate for out-of-plane mode attenuation.