The properties of SMA (Shape Memory Alloys, smart materials) are associated to a first order phase transition named martensitic transformation that occurs between metastable phases: austenite and martensite. At higher temperature phase or at lower stress the austenite is the metastable phase. The martensite appears at lower temperature phase or higher stresses. The hysteresis of the transformation permits different levels of applications, i.e., in their use as a damper. Two types of applications can be considered in damping of structures in Civil Engineering. The first one is related to diminishing the damage induced by earthquakes. The second one is a reduction of oscillation amplitude associate to an increase of the lifetime for the stayed cables in bridges. Different fundamental behavior of the SMA needs to be guaranteed in each case.