Advanced composite structures with integrated sensors and actuators are becoming increasingly important due to the demand for very large, low-mass space structures. This paper focuses on the finite element analysis of shell structures with thin piezo-electric layers bonded to the surfaces. A finite element formulation taking the piezo-electric effect into account is given and a finite shell element is presented, allowing for the computation of these advanced composite structures. The dynamic matrix equation accounting for the piezo-electric material response is formulated and found to have the same form as the well-known equation of structural dynamics. By using the second or direct method of Lyapunov, a control law is derived, which is used in vibration control and ensures asymptotic stability. A numerical example is given to show the accuracy of the finite element, as well as the efficiency of the algorithm. © 1991.