Model predictive control (MPC) is a control method which uses future predicted outputs of a system to determine the inputs to the system. The predictive control methods are well suited for systems where model identification is difficult and expensive or where the parameters of the plant and environment change frequently. All of the predictive control methods are tracking controllers by nature. Most predictive control algorithms have been developed for use in the process control industry for set point tracking. The main advantage of MPC controllers over other tracking controllers is that they can act in advance of the actual time when there is a change in the set point. The use of predictive control for vibration suppression of smart structural systems investigated in this paper. For vibration suppression purposes, the set point of the predictive control is set to zero and the effect of the disturbances on the system performance is to be minimized. Many of the predictive control algorithms do not allow for the system output to substantially depart from its predicted values. However, the predictive controller proposed by Gawronski allow the prediction to converge to the correct value after a disturbance has occurred, even if the disturbance causes the output to oscillate as in the vibrations of smart structures. We have proposed a modification to the predictive control algorithms by incorporating the prescribed degree of stability concept in the design. In order to demonstrate the capabilities of the proposed predictive controllers, we have designed and implemented the controllers on two simple test structures. The experimental closed-loop response of single input/single output and multi-input/multi-output structures is presented in the paper. The response of the predictive control system is compared with that of Linear Quadratic Gaussian controllers. The advantages and limitations of the predictive controllers are discussed in the paper.