An analytical solution of a two dimensional bow and stern flow model based on a flat ship theory is presented for the first time. The flat ship theory is a counterpart to Michell’s thin ship theory and leads to a mixed initial boundary value problem, which is usually difficult to solve analytically. Starting from the transient problem, we shall first show that a steady state is attainable at the large time limit. Then the steady problem is solved in detail by means of the Wiener Hopf technique and closed form farfield results are obtained for an arbitrary hull shape. Apart from providing a better understanding of the underlying physics, the newly found analytical solution has shed some light on solving a longtime outstanding problem in the engineering practice of ship building, the optimisation of hull shape.