A fluid-structure interaction (FSI) is the interaction of some movable or deformable structure with an internal or surrounding fluid flow. FSI is the essential consideration in the design of many engineering systems; e.g. aircrafts, nuclear and piping system. In this paper firstly the orders of accuracy of finite difference method were tested and secondly two types of algorithms were evaluated to obtain the displacement and transient pressure for pipe conveying fluid under transient condition, From the study it reveals that the fourth order of accuracy is the more compatible for this combination of equations. The transient pressure calculated by algorithm1 and algorithm2 were compared with experimental result to find that algorithm2 has a full agree with experimental data.