The fluid motion raised by a ship has been theoretically investigated by various researchers under the assumption that the deformation of the surface of water is negligibly small. But results obtained under this assumption do not wholly agree with experimental one, Then it seems to be indispensable to regard on the finite deformation of the free surface. Dr. Kreitner made some considerations on this problem for one dimensional cases. In the present paper the writer gives an expanded theory for the two dimensional problem uuder the assumption that the vertical acceleration can be neglected in comparison with that of gravity. The results obtained from this theory shows that there is a critical range of finite extension for the fluid motion even when the breadth of the water way is not restricted. This result could not be obtained from the linearised theory considering the surface deformation so small that it could be neglected.