This paper gives a theoretical analysis of storm surges generated on a continental shelf by moving wind fields; surges generated in the ocean and propagated on to the shelf are also investigated. A continental shelf of uniform depth and width, bounded by a long straight coast and connected with an infinitely deep ocean, is considered. In studying the motion of the shelf sea, bottom friction and Coriolis force are taken into account, and it is supposed that conditions are the same in all vertical sections normal to the coast. The theory is applied to the problem of storm surges on the west coast of the British Isles. It is shown that these surges are generated by wind fields, associated with moving depressions, acting over the sea of the continental shelf to the south of Ireland. In two cases the observed surge at Milford Haven has been reproduced satisfactorily by the theory.