In this paper, we adopted the traffic flow model with the consideration of the accident probability, which is recently developed by Tang et al. （Tang T Q, Huang H J, Xu G 2008 Physica A 387 6845）, to study the effect that the accident position has on shock and rarefaction wave. The simulation results show that our model can perfectly reproduce the effects that the accidental position produces on the two traffic waves and the effects are completely related to the accident position.