Using finite elements, a simulation is prformed for the pipe systems to investigate free vibrational characteristics, that is natural frequencies, considering the intial tension due to the velocity and the pressure of the inside fluid flow. To confirm the program developed in this study, the results are compared with the results of commercial software ANSYS. When the initial tension is neglected in curved pipes, the natural frequencies are reduced as flow velocity increases, and the rapid decreases of the natural frequencies took place. However, when the initial tension is taken into account, the natural frequencies are not changed with the change of the flow velocity. In free vibrational simulation of pipe systems, it is necessary to calculate the initial state force due to the velocity and the pressure of the fluid flow from the equilibrium first, then the force should be included in the equation of motion of the systems to get more accurate natural frequencies.