The singular perturbation problem of the self-similar flow around the cusped-bow ship with the circular cross-sections is discussed in the limit of vanishings of the small dimensionless parameter F , which corresponds to the Froude number. The asymptotic expansions of the velocity potential are constructed in both domains near and far from the body. In the near field, it is shown that the local waves only appear in the formal solution expanded in the ascending even powers of F . In the far field with the large spatial extent of O (1/ F ²), the solution satisfying the homogeneous free-surface conditions with the no appearance of the parameter F contains both the local waves and the free waves to be added up to the near field solution. The wavy potential of O ( F ⁷) obtained by the WKB approximation method of the solution with the satisfaction of matching to the far field solution is supplemented to the formal near field solution.