The article illustrates an approach to the passive vibration control of thin plates utilizing prestressed superelastic shape memory alloy (SMA) wires. The SMA wires can freely slide within protective sleeves that are either embedded within the structure or bonded to its surface. The vibration control mechanism combines an effective continuous elastic foundation representing the support provided by SMA wires to the structure with the energy dissipation as a result of the hysteresis occurring in the wires. The other approach to the vibration control employs superelastic wires attached to the structure at discrete points. The mathematical formulation of the problem presented in the article can be adopted for a rigorous computational analysis. In particular, a closed form expression is obtained for the loss factor in large aspect ratio plates supported at the midspan by a system of parallel SMA wires. As follows from numerical examples presented for such plates, the proposed method offers a significant damping, far exceeding that observed in conventional engineering structures. © 2011 Springer Science+Business Media B.V.