© 2016 The Authors.The main objective of this paper is to investigate theoretically and numerically how much interactions are expected between two ships travelling in waves. The theoretical estimation is based on asymptotic far-field wave patterns produced by a translating and oscillating source. The far-field wave pattern is governed by the parameter τ=ωeu0/g; For values of the parameter τ>0.25 there exist a fan-shaped quiescent region in front of the vessel. As τ increases, the range of the fan-shaped quiescent region will be expanded. The critical line between the quiescent and wake region can be estimated by the asymptotic expressions theoretically. It is expected that there is no hydrodynamic interaction if the two ships are located in each other's fan-shaped quiescent region. But due to the near-field local waves produced by the 3-D ships, the critical line could be different from that estimated from asymptotic wave pattern. Therefore, we developed a 3-D panel method based on Rankine-type Green function to investigate the hydrodynamic interaction effects for several combinations of parameters, including oscillation frequency, forward speed and transverse distance between two ships. Finally, the critical line calculated numerically was presented and compared to the theoretical estimation.