Abstarct: In this thesis, smart piezoelectric structures and two main techniques for vibration control of this structures is studied: 1) Vibration suppression of structures using piezoelectric passive shunt circuit, 2) Active vibration control of structures using piezoelectric sensors and actuators. Being new field of research, there is still some confusion in the definitions and applications of these structures which is tried to get cleared in this thesis. But the main objective of this study is to find applicable and simple ways for modeling and control of these structures with two mentioned techniques. For this reason, after defining the finite element equations of the closed loop systems, ANSYS is used to model the structures while the control actions are integrated with the ANSYS finite element model by APDL. A cantilever beam having symmetrically bonded piezoelectric patches is considered as a simple model of a smart structure. To study the passive response of the piezoelectric structures under shunt damping, harmonic analysis within the range of the natural frequencies of the structure is used. To investigate the active response of the structures having piezoelectric sensors and actuators, transient analysis is used and the response of the structure to the free and forced vibrations is studied. The response of the structure to a moving load is also studied.