A mathematical model aiming to describe the stern flow accompanying the large scale bilge vortices is proposed based upon vortex theory in inviscid fluid. The introduction of vector potential makes clear to obtain a vortex singularity distribution kinematically equivalent to the flow around the full body. As the first trial, the double-body flow without free vortices is analysed using the surface vortex lattice method to which the correction, analoguous to the Prandtl's lifting surface correction, is applied. Results are in fairly good agreement with those of Hess & Smith method.