In ship motion stability, generally, capsizing occurs due to the following effects: loss in directional control such as in broaching-to; loss in stability (pure loss of stability) and transient effect like parametric excitation. It is generally accepted that hydrodynamic forces due to waves are dominant that cause vessels'' capsizing. It is generally accepted that numerical simulation using computers are reliable to study the ship motions. As a result, the 6 degrees-of-freedom time domain simulation will be used to study the ship motions especially the large amplitude motions. In this paper, we adopt three classes of numerical approach namely explicit Runge-Kutta, implicit Runge-Kutta and Rosenbrock-type Runge-Kutta methods in order to verify the effect of stiffness in ship motion simulation.