A shunted piezoelectric is a device to suppress vibration consisting of a piezoelectric material and a shunt circuit connecting between two electrodes of the piezoelectric material. The sensitivity of damping performances is analyzed for passive shunted piezoelectrics: a resistive, a series resonant, and a parallel resonant shunted piezoelectric. The parameters that affect their damping performances are Young's moduli of a base structure and a piezoelectric material, a piezoelectric coupling coefficient, an electric permittivity of a piezoelectric material, and resistance and inductance of a shunt circuit. A loss factor is selected as a performance index for the damping and formulated for each type of shunted piezoelectric. For an aluminum beam with symmetrically bonded piezoelectric patches, the sensitivity of the loss factor is evaluated with respect to the system parameters. For a resistive shunted piezoelectric, a piezoelectric coupling coefficient has the largest effect on the damping performance. For resonant shunted piezoelectrics, an increasing electric permittivity of the piezoelectric material has the greatest effect on the damping performance. As a whole, the sensitivities for both resonant shunted piezoelectrics are in the similar level and they are much larger than that for a resistive shunted piezoelectric. Using the sensitivities to parameter values, the estimation method for the sensitivity with respect to varying operating conditions such as the temperature change is presented.