In this paper we present an entirely random traffic flow model by introducing brake, creation and disappearance probabilities into 1D local interactive cellular automota. By means of epuilibrium spin theory, we find that when Pin=Pout≠0, the final density of the model is ρｔ＝0.5 and indepen-dent of initial density distribution. When the conditions Pin+Pb=1 and Pin=Pout are satisfied, we get a simple “linear” traffic flow model that displays long distance correlation under the condition |1-2Pin|=1 and leads to a serious traffic jam. The cemputer simulation results agree with the the-oretical prediction.