A mechanical model for pseudoelastic behavior of NiTi wires is proposed with the aim to predict the behavior of Shape Memory Alloys(SMA) damping wire elements in model structures. We have considered at first a simple linearwise stress-strain relationship to describe the basic isothermal behavior of the SMA members. Then, this basic model is modified in order to include the effect of the strain rate. The model is based on detailed experimental characterization performed on a Ni rich NiTi superelastic wire which included the study of the localized character of the deformation and the local heat generation associated with the stress induced martensitic transformation occurring in these alloys. Heat conduction along the wire and heat interaction with the surroundings was also considered. In that way, the resulting local temperature field around the transformation front is assessed and its effect on the progression of the transformation is evaluated. It is shown how the simple mechanical model reproduces the global mechanical behavior, including the existence of a maximum in the damping capacity with the transformation rate.