Accurate prediction of wave interaction with a floating elastic plate of small thickness has considerable significance in ocean engineering. We propose a hybrid boundary element and finite difference method for a plate of arbitrary shape. It is found that the plate has an obvious effect on the three-dimensional wave fields, and a large part of the disturbed wave appears around the direction of the incident wave. Like an elastic plate in vacuum, resonant behavior can occur for a plate floating on water. But, the peaks at the natural frequencies will be very large, instead of infinity, due to the wave radiation damping.