The first report dealt with the forward sliding and the backward tumbling as the most dangerous consequences of wheelchair use on board a passenger ship. The present paper proposes a dynamical model of wheelchair behaviour in an oscillatory environment. To simplify the movement of the wheelchair, a ball-caster is introduced in place of the ordinary caster wheel. A test dummy is used to eliminate the effect of human-body's intra- and inter-subject variability. Simultaneous differential equations expressing the wheelchair motions are solved by the 4th order Runge-Kutta method sequentially. A series of computer simulation is carried out for the wheelchair's motion on a flat and/or an inclined floor and the response in an oscillatory environment. The model proposed can also estimate the necessary driving torque to run along a given course. The effect of a movement of the centre of gravity was examined. A manually propelled wheelchair was assumed in this paper, and the model can be applied to a motorised wheelchair. The authors conclude that the proposed dynamical model is useful to estimate the wheelchair's response in an oscillatory environment quantitatively as well as qualitatively.