The linearization of boundary conditions both for ship surface & free surface often gives rise to discussion when we seek the relation between ship forms and their wave-making resistance especially of displacement ships. Inui's improvement for ship surface condition is well known as a double model conception. However it still neglects partially the free surface effect except for exactly corresponding zero Froude number case. An extention of his idea is examined here to build up a more exact theory by introducing a higher or the second order ship surface approximation taking the whole free surface effect into account. His approach is called stream-line persuit method or inverse method because not ship forms but their equivalent source or doublet distributions are determined first with sometimes the aid of variational treatment of wave-making resistance formula expressed by functional singularity distribution. In this paper, two concrete non-zero Froude number hulls corresponding to K ₀ L =14 are obtained to sereve for streamline observation, resistance test and wave pattern comparison. As the result it finds that 2nd order approximation of hulls contributes to the improvement in the theory of wave-making resistance, provided that some disagreement of ship surface condition still remains near the bow.