Fluid-structure interaction (FSI) problems are increasing in various engineering fields. In this thesis, different cases of FSI in two-and three-dimensions (2D and 3D) are simulated using OpenFOAM and foam-extend. These packages have been used to create a coupling between fluid and solid.The vortex-induced vibration (VIV) phenomenon of flow past a circular cylinder is studied using PIMPLE algorithm for pressure-velocity coupling. This VIV study is restricted to incompressible flow simulation at a Reynolds number (Re) of 100. The changes of drag and lift coefficient values depend on the study case and the spring-massdamper system for the flow past a free oscillatory cylinder. The free vibrating cylinder examined in one-degree-of-freedom (1DOF) and two-degrees-of-freedom (2DOF) systems with linear damping and spring properties. Both will affect the behaviour of the cylinder within the flow with some noticeable differences. The response time of the cylinder and the drag coefficient are the most affected by the spring and damper.