A study has been made of piezoelectric shunts using a piezoelectric element shunted with a parallel resistor and inductor circuit for passive structural damping and vibration control. It is found that under the optimum tuning condition, the peak amplitude of the displacement versus frequency curve of a structural mode decreases with the increase of the shunt resistance. It becomes a plateau at the optimum resistance. When the resistance increases further, the middle of the plateau continues to decrease, but two humps appear around the plateau shoulders. They increase with further increase of the shunt resistance. Changes in structural parameters, mass or stiffness, and incorrect shunt inductance also affect the displacement versus frequency curve. Both will distort it from a plateau shape under the optimum condition to that showing a hump on one shoulder of the plateau. If the mass increases (or decreases), the hump appears on the left (or right) shoulder. It becomes larger and moves away from the plateau for larger mass change. For the case of incorrect inductance, when the inductance is larger (or smaller) than the optimum value, the hump appears on the right (or left) shoulder. It moves towards the center of the plateau with further deviation of the inductance.