For ships navigating in ice floe fields, ship–ice–wave interactions may affect ship performance and ice impact forces. This paper presents an approach to evaluate the cross-coupling added mass and hydrodynamic damping between a passing ship and a free-floating small/medium size ice floe based on the boundary element method (BEM). The influences of added mass and hydrodynamic damping are explored for different wave frequencies and headings. Results are presented for a regular waves scenario whereby a tanker progressing at a slow speed is passing by a free-floating ice floe modeled as a round disk. Radiation and diffraction potentials of the interacting floating bodies are linearly superimposed to reflect the influence of hydromechanical coupling on responses. Parametric analysis of response amplitude operators (RAOs) indicates that the cross-coupling terms of added mass and hydrodynamic damping are of the same order of magnitude as those of the ice floe but smaller by one or two orders of magnitude than those of the ship. It is concluded that hydrodynamic interactions primarily influence the motions of the ice floe and are significant attributes in terms of suitably idealizing ship–ice system dynamics.