Objectives  The strip method is widely used in the sea-keeping design of ships, but the hydrodynamics are only evaluated for the mean-hull position, so heaving, pitching and rolling motions are not essentially coupled.

  Methods  For the effective coupling of hull heaving, pitching and rolling motions, based on the extensive pitch angle and increased draught, and the analytical expression of the instantaneous wave surface equation under the hull coordinate system, the calculation formula of pressure distribution under the wave surface is amended under the condition that the pressure at the wave surface is zero(Smith effect). Based on the wave surface equation and pressure distribution correction formula, the calculation method for obtaining the hydrostatic force on hull sections under an instantaneous wave surface and Froude-Krylov wave excitation force is given. Inertial hydrodynamic force and damping force are calculated by empirical formulations. As such, the heaving, pitching and rolling coupling dynamic equations are derived via the time variants of the coefficients, and calculation software is developed on the basis of surface area computing technology of AutoCAD.

  Results  The simulation results show very clear characters with the linear method on small wave height, the rolling amplitude frequency response very evidently shows non-linear effects for heavy seas, and the rolling-yawing can also be seen in the wave direction in the resonance region.

  Conclusions  This approach can be useful for predicting sea-keeping performance in heavy seas, and the developed software may be used for evaluating sea-keeping hull forms.