Inspired by the vibrations of aquatic plants such as seaweed in the unsteady flow fields generated by free-surface waves, we investigate a novel device based on piezoelectric plates to harvest energy from oscillatory cross flows. Towards this end, numerical studies are conducted using a flow-structure-electric interaction model to understand the underlying physical mechanisms involved in the dynamics and energy harvesting performance of one or a pair of piezoelectric plates in an oscillatory cross flow. In a single-plate configuration, both periodic and irregular responses have been observed depending on parameters such as normalized plate stiffness and Keulegan–Carpenter number. Large power harvesting is achieved with the excitation of natural modes. Besides, when the time scale of the motion and the intrinsic time scale of the circuit are close to each other the power extraction is enhanced. In a two-plate configuration with tandem formation, the hydrodynamic interaction between the two plates can induce irregularity in the response. In terms of energy harvesting, two counteracting mechanisms have been identified, shielding and energy recovery. The shielding effect reduces plate motion and energy harvesting, whereas with the energy recovery effect one plate is able to recovery energy from the wake of another for performance enhancement. The competition between these mechanisms leads to constructive or destructive interactions between the two plates. These results suggest that for better performance the system should be excited at its natural period, which should be close to the intrinsic time scale of the circuit. Moreover, using a pair of plates in a tandem formation can further improve the energy harvesting capacity when conditions for constructive interaction are satisfied.