The current effort attempts to construct a non-linear 6-DOF mathematical model for ships in order to simulate the behaviour of a sailing boat in downwind and following regular waves. The purpose is to observe interesting dynamical phenomena such as surf-riding and broaching-to, including their evolution in the phase plane. The hydrodynamic model developed despite some additions, is mainly based upon earlier works in the area by the authors [1–4] that include also hydrodynamic memory effects, whereas the wind modelling considers steady wind magnitude and uses available precalculated force coefficients for various apparent wind and heel angles [5–7]. It should be noted that the model is constructed in a computational environment that allows bifurcation analysis and is suitable in the future for conducting continuation analysis. Such peculiarities are explained in detail in this article. Moreover, preliminary results are presented that depict these complex dynamical phenomena for each of the different behavioural patterns. All these will constitute the starting point of a prospective more through bifurcation analysis.