In this paper a submerged horseshoe vortex under a free surface is discussed and the algebraic expression of the wave elevation is obtained. From this expression, some characteristics of the ship wave are described. There exists a smooth region near θ = 0°, but when the uniform stream passes the other singularities (source, sink, doublet, etc.)there is no smooth region. The mechanism of synthetic aperture radar (SAR) images of the narrow ship wakes is also explained.