The paper presents an approach to passive vibration control of shear deformable and thin plates. The first of two methods of vibration control employs prestressed shape memory alloy (SMA) wires embedded in sleeves attached to the surface of the plate. The spacing between the wires can be arbitrary and variable enabling the development of a SMA support system for maximum control with minimum additional weight. The other method considered in the paper utilizes SMA wires supporting the plate at strategically selected points. The mechanism of passive control includes two components: (1) SMA wires prestressed as a result of constrained phase transformation act as an elastic foundation with a variable stiffness and (2) energy dissipation occurs as a result of hysteresis in superelastic wires vibrating together with the structure. As follows from examples, it is possible to achieve a significant reduction of the vibration amplitude over a broad spectrum of driving frequencies using any of two methods considered in the paper.