Abstarct: Fluid-structure interaction (FSI) occurs when the dynamic water hammer forces; cause vibrations in the pipe wall. FSI in pipe systems being Poisson and junction coupling occurring due to water hammer has been the center of attention in recent years. It causes fluctuations in pressure heads and vibrations in the pipe wall. The governing equations of this phenomenon include a system of first order hyperbolic partial differential equations (PDEs) in terms of hydraulic and structural quantities. In present, various numerical models, which include the finite difference methods (FDM), finite volume methods (FVM), the finite-element methods (FEM) or a combination of these methods has been used to solve the equations FSI. Historically, some methods such as Method of Characteristics (MOC) and Godunov's scheme have been successfully used for solving these equations but these methods suffer from restrictions. In MOC, steps need to certain fit together in time and space, and that is why the intervals should be selected depending on the magnitude of the problem. In Godunov scheme, Riemann problems are solved and hence field-by-field decompositions are used so run times are too much. In this study, Lax-Friedrichs, Lax-Wendroff, Lax-Wendroff with nonlinear filter, Nessyahu-Tadmor and MacCormack methods were implemented as a good and efficient methods for considering hyperbolic system of differential equations so we solved two problems in this field and the computational results are compared with those of the Method of Characteristics (MOC), and also with the results of Godunov's scheme to verify the proposed numerical solution. The results reveal that the Lax-Friedrichs and Nessyahu-Tadmor schemes have good agreement with results of MOC and Godunov in FSI. In water hammer, all of proposed methods can predict discontinuous in fluid pressure with an acceptable order of accuracy in gradually closesure but in suddenly closesure, Lax-Wendroff, Lax-Wendroff with nonlinear filter and MacCormac methods fail to predict discontinuous in fluid pressure and simulate with a lot of fluctuations in heads in discontinuities.