Two-dimensional thin plates are widely used in many aerospace, automotive and marine applications. Vibration attenuation can be achieved in these structures by attaching piezoelectric elements on to the structure integrated with shunt damping circuits. This enables a compact vibration damping method without adding significant mass and volumetric occupancy, unlike the bulky mechanical dampers. Practical implementation of shunt damping technique requires accurate modeling of the host structure, the piezoelectric elements and the dynamics of the shunt circuit. Unlike other studies in the literature of piezoelectric shunt damping, this work utilizes a multi-modal equivalent circuit model (ECM) of a thin plate with multiple piezo-patches, to demonstrate the performance of shunt circuits. The equivalent system parameters are obtained from the modal analysis solution based on the Rayleigh-Ritz method. The ECM is coupled to the shunt circuits in SPICE software, where the shunt configuration consists of three branches of electrical resonators, each tuned to one vibration mode of the structure. Using the harmonic analysis in SPICE for a range of excitation frequencies, current output of each ECM branch is calculated for open-circuit and optimum shunt circuit conditions. The current of ECM branches are then converted to the displacement outputs in physical coordinates and validated by the finite-element simulations in ANSYS. It is shown that the vibration attenuation of a vibration mode can be successfully achieved when there is a reduction in the corresponding current amplitude of the ECM branch. This correlation can be utilized in the design of efficient linear/nonlinear shunt circuits.