Abstarct: Fluid-Structure Interaction (FSI) issues such as Poisson and Junction coupling and their effects on water hammer results in important piping systems have been in attention in recent years. These effects cause vibration in pressure heads and displacements of pipe wall. Considering the behavior of viscoelastic (VE) materials in dampening and energy dissipation, the main purpose of this research is analysis of water hammer and modeling of fluid-structure interaction in a pipe line (made of elastic or viscoelastic materials) with viscoelastic supports. In this study in order to describing the behavior of viscoelastic substances, the generalized Kelvin-Voigt mechanical model and the integration form of its constitutive equations has been used. For numerical solution of the convolution integral caused by viscoelastic behavior, a numerical approximation was used in accordance with unknowns of the current time step and the known values of the previous time step. The hydraulic equations were solved by the method of characteristic (MOC) and the structural equation that has appropriately been derived for implementation of boundary condition of VE support are solved using the finite element method (FEM) in the time domain. The results showed that using of VE supports with appropriate properties and numbers are very effective and efficient in damping and decreasing the displacement of pipe wall, vibration of pressure heads caused by FSI and also dampening the pressure heads over time, especially in elastic pipes. They can also significantly reduce the stress and its rate of changes in the pipe and its supports over the time and improve the performances of the pipe structure against the fatigue phenomenon. In addition, the maximum pressure head in VE pipes that occurs at first cycle, unlike the elastic pipes, can be decreased.