Abstarct: The fluid-structure interaction (FSI) and related issues, as well as the effects of water hammer phenomenon on pipe systems have always been considered. Because these effects are observed as vibration and increase in the pressure and displacement of pipe wall. Regarding the properties of viscoelastic materials in damping and energy dissipation, the purpose of this study was to model the viscoelastic supports with axial deformation mechanism due to the forces (horizontal) applied to the supports to investigate their effects on FSI, during the water hammer phenomenon in straghit pipe systems (viscoelastic) with variable poisson ratio. In this thesis, poisson and junction coupling mechanisms of FSI are considered. Viscoelasticity behavior of the pipe wall and the supports is described with the generalized Kelvin-voigt mechanical model. By providing boundary conditions for modeling different types of viscoelastic supports in the valve location and along the pipe, the governing equations are solved by the full MOC method in the time domain. The results are plotted as a time-pressure history at a specific point in the pipe and compared with the results presented in previous authoritative sources. The results of this study indicate that due to the damping properties of viscoelastic materials, considering variable poisson ratio for viscoelastic pipes, did not cause significant changes in the pressure head due to water hammer, compared to its constant consideration.