The straight running behaviour of a passenger coach is investigated for the cases of the wheelsets considered as elastic and as rigid bodies. The model used for this investigation includes rotating elastic wheelsets modelled in an efficient way for the computation and a nonlinear wheel-rail contact. The behaviour below and beyond the critical speed is studied for the configuration of rigid and elastic wheelsets. The comparison of the simulation results show a distinct influence of the structural elasticity of the wheelsets, especially a drop of the critical speed.