Abstarct: Fluid-structure interaction in pipe systems in which the dynamic behaviour of pipe systems following water hammer is being studied has been the subject of attention in recent years. In addition, the application of viscoelastic pipes is thriving in various piping systems due to their numerous advantages. Column separation is also a very considerable issue as it can bring about devastating effects. Describing the mathematical modelling and providing the appropriate numerical tool for the FSI in viscoelastic pipe systems with taking into account the column separation phenomenon was the main aim of this thesis. Governing equations were derived for the first time in this research and were solved using two different suggested methods: full method of characteristics (full MOC) and method of characteristics-finite element method (MOC-FEM). Furthermore, the solution baxsed on MOC-FEM was extended to provide a useful tool in solving systems with various types of boundary conditions. In the investigation of column separation, the simplest method called discrete vapour cavity model (DVCM) was employed. It was chosen to be included in FSI analyses in viscoelastic pipes due to its simple concept and easy implementation. From physical point of view, in a water hammer problem, the viscoelastic behavior results in retarded strains in radial and axial directions. Axial strains are generated only if the FSI effects are taken into account. In this research, the governing equations for modeling the retarded axial strains were derived and their interaction with the hydraulic equations was investigated. In obtaining the final solvable differential equations, the retarded strains were treated using exxpressions in the form of convolution integrals and then were approximated with appropriate relations. The approximation provides recursive functions of unknowns for the calculation of convolutions integrals. The recursive relations can then be employed in conjunction with the conventional numerical solutions of FSI. Manifestation of the robustness of two numerical methods being full MOC and MOC-FEM for investigation of viscoelastic pipes following a water hammer was the main conclusion of this work. It was also demonstrated that the FSI effects in viscoelastic pipe systems were more significant than in elastic pipes. This conclusion was drawn after verifying the numerical schemes in different stages and then investigating several case studies. Substantial damping and less cavitation were the other crucial deductions which can be inferred from the provided head results.