Abstarct: One of the most important issues in analyzing pipeline networks is simulating fluid structure interaction (FSI) caused by the unsteady flow in networks. This phenomenon involves transmission of energy and momentum between the pipeline's structure and the fluid and is normally produced by intensive change of flow rate and fluid pressure or mechanical factors in pipeline systems. As the governing equations are hyperbolic in this phenomenon, for analyzing and simulating this interactional feature, the method of characteristics (MOC) was used. But due to some reasons like encountering with nonlinear equation systems or existence of complex terms in equations, using MOC method despite of its high efficiency and precision and sometimes need for additional numerical modeling which makes it more complicated, it has some limitations. It is therefore, necessary to consider and compare the ability of this method with other numerical methods more accurately creating more attention of researchers toward using other numerical methods for solving hyperbolic systems of differential equations similar to those of fluid structure interaction. In this study, Godunov method was implemented as a good and efficient method for considering hyperbolic system of differential equations so we solved one of the famous laboratories reference problems in this field and compared obtained results with Godunov method applied for previous results of MOC. The compatibility of these results, showed the ability of Godunov method in the field of analyzing hyperbolic system of differential equations.