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The construction of a safety society is important all over the world. Many peoples died and were injured the derailment accident of the railway on April 25 in 2005. The reliability of railway system was lost. If some support systems for railway drivers will be developed by the brake systems, such serious accidents will reduce. On the other hand, no studies have shown about the transfer function of the driver and the brake systems concerning safety in the railway to now. This paper shows that stability and safety about the railway vehicles controlled the railway driver. The driver model used the model proposed by Inguchi et al., and used the transfer function that consisted of the proportion, differentiation and the integration operation. From the simulation results, derivative gain of transfer function of driver model is important in the brake and vehicle dynamics.