Superelasticity, a unique property of shape memory alloys (SMAs), allows the material to recover after withstanding large deformations. This recovery takes place without any residual strains, while dissipating a considerable amount of energy. This property makes SMAs particularly suitable for applications in vibration control devices. Numerical models, calibrated with experimental laboratory tests from the literature, are used to investigate the dynamic response of three vibration control devices, built up of austenitic superelastic wires. The energy dissipation and re-centering capabilities, important features of these devices, are clearly illustrated by the numerical tests. Their sensitivity to ambient temperature and strain rate is also addressed. Finally, one of these devices is tested as a seismic passive vibration control system in a simplified numerical model of a railway viaduct, subjected to different ground accelerations.