Abstract. There have been published many papers and several reviews on the application of SMA's as damping devices in civil engineering by using the pseudo-elastic effect, but they are difficult to apply because the behaviour of the alloys is not carefully analyzed. In particular, the summer-winter temperature effects, aging long time at low temperature, self-heating or residual strains requirements for the given applications are rarely well established. In this work, we analyze and compare two cases, the damping of earthquake effects on relatively small structures as family homes, and the damping of stayed cables in large bridges. The requirements for the materials are different, and in each case a different commercial alloy with appropriate conditioning might provide acceptable answers. To confirm the usefulness of the dampers, the hysteretic behaviour of two SMAs (CuAlBe and NiTi) has been analyzed, and later modelled and introduced in finite element codes for the simulation of structures. The behaviour of the structures without and with dampers have been analyzed and compared. Also, some realistic experiments with cable 1 in the ELSA Joint Research Centre of the EU in Ispra have been done with NiTi wire of 2.46 mm diameter as damper, to compare with simulations.