For the mechanism of ship capsizing, we can generally consider that it`s caused due to pure loss of stability, parametric oscillation(low cycle resonance) of ship in waves and the broaching phenomena. Among them, low cycle resonance occurs due to the dynamic change of righting arm with respect to the relative position of ship to waves. The dynamic change depends on the encounter period of a ship in following waves. This paper discusses the following items : (1) An analytical expression of GZ curve varying with respect to the relative position of ship to waves, (2) Non-linear equation of motion describing low cycle resonance, (3) The effects of righting arm, stability range and encounter period on low cycle resonance.