This study deals with a simulation method for a transient response of fluid transmission lines. In the previous report of this study, we proposed a faster and more convenient method for simulating the transient response of fluid rigid lines. In the same report, furthermore, we proposed a method for approximating in high accuracy an exact mathematical model of fluid transmission lines, which is formulated by a distributed parameter system, by a finite order rational polynomial. In this report, in succession, we deal with a similar method as before for simulating a transient response at arbitrary position of transmission lines, including not only rigid tube but also viscoelastic tube. It could be confirmed that simulated results of pressure and flow rate responses at arbitrary pipe position were obtained in considerably high accuracy by attaining a faster simulation.