Although linear ship motions theory is sufficiently accurate in predicting the motions of a ship/offshore platform in irregular seas, it cannot capture many of the nonlinear dynamic phenomena (e.g., parametric resonance) which might be very important in the design phase. In order to accurately simulate the motions of a structure, one has to resort to 6 degrees of freedom coupled nonlinear time-domain simulations. This paper presents the theoretical development of such a tool (called SIMDYN) which solves the nonlinear equations of motion while considering the large-amplitude rotations of the body. It also accounts for the nonlinearity of Froude–Krylov and hydrostatic forces. The validity of the developed tool is verified by comparing the predicted motions against the linear theory for small amplitude motions. The paper also shows an example of parametric roll simulation of a container ship to demonstrate the ability of the tool to capture nonlinear phenomena accurately. This tool is then applied to perform 30 3-h coupled simulations of a container ship in head seas, and the resultant time series from each simulation are analyzed to study the ergodicity of parametric roll in irregular longitudinal seas.