A Rankine source method is extended and applied to ship–ship interaction problems. The method covers the nonlinear steady flow and linear seakeeping in the frequency domain. The nonlinear steady flow solution accounts for the nonlinear free-surface conditions, ship wave, and dynamic trim and sinkage. Periodic flow due to waves is linearized with respect to the wave amplitude, taking into account interactions with the nonlinear steady flow following Hachmann approach, which considers the steady perturbation potential as constant in the body-fixed reference frame. This is advantageous for the prediction of ship motions at moderate to high Froude numbers. In this context, a new formulation of the boundary condition for the multibody case is derived. Two examples are considered, overtaking in calm water and replenishment at sea. For a feeder vessel overtaken by a container ship, horizontal forces and yaw moment are computed and compared with reference data. As an example of replenishment operation, interaction between a frigate and a supply vessel is studied. Ship motions are computed for two relative positions and three forward speeds and compared with model test data for the largest forward speed. The Rankine source method proves as more accurate compared with a zero-speed free-surface Green function method.