When the prescribed body position is one of equilibrium, we may ascertain if it is a stable position, an unstable position or a neutrally stable position. The stable position occurs when a body subjected to a small disturbance from an equilibrium state tends to return to that state. The neutrally stable position occurs when the body reaches and remains in its new position following the disturbance. The unstable position occurs when, following the disturbance, the body tends to increase its shift away from equilibrium.

According to the above definitions, the horizontal disturbance force or moment may cause the free-floating body to translate or rotate horizontally and remain in a new equilibrium position, so that the surge, sway, and yaw motion modes are in the neutral equilibrium states. The equilibrium condition for heave motion of a free-floating body which pierces the water surface is always stable. However, the equilibrium conditions of roll and pitch for the same body may be stable, neutral or unstable, and are required for further investigation. These conditions are referred to as the transverse and longitudinal stabilities for ship-like structures.