A periodic wind produces an oscillating response when it blows across an ocean overlying a continental shelf. In this paper, the response of a frictionless, horizontally non-divergent ocean to a wind system which travels along the shelf is considered. It is shown that the periodic response produced by such wind systems may have a resonant non-linear interaction with shelf waves whose frequency is close to half that of the wind. The theory may have applications to east-west continental shelves (for example, the south coast of Australia) when strong weather systems move eastward along the shelf.