Vibration control using combination of piezoelectric material and electrical circuits can remove the vibration energy from the host structure. The need for passive damping techniques arises to avoid the complexities and energy requirements associated with other vibration control techniques. Passive damping technique for reduction of vibration of structures by introduction of shunted piezoelectric patch is presented in this study. Finite element analysis is performed for a cantilever beam with shunted piezoelectric patch on it. The prediction of the model is validated against experimental published results. The obtained results demonstrate the feasibility of using piezoelectric patches with passive shunting as effective means for damping out the vibrations. The aim of this research work is the advancement of the coupled field analysis for structural vibration control with advanced methodology and to promote the design and analysis activities in the field of passive vibration control techniques using smart structures. Results obtained showed up to 86% reduction in the amplitude of the host structure which shows good agreement with published experimental results.