A free surface flow is a group of multiphase flows where an interface separates two immiscible fluids. One of the critical issues in these flows is the presence of a bluff body near the free surface, which has many applications in fluid flow pipelines, offshore structures, autonomous underwater vehicle, marine turbines, energy harvesting, and maintenance of oil and gas platforms, and submerged tunnels. Due to the interaction between the free surface and the immersed body, the simulation of these problems is complex and time-consuming. In this thesis, the effect of the presence of a stationary and moving cylinder (rotating and also under the effect of vortex-induced vibration) on the deformation of the free surface as well as the hydrodynamic and heat transfer characteristics of the cylinder have been investigated. The simulation is conducted by using ANSYS-FUENT software. The free surface analysis is modelled by the Eulerian-Eulerian approach and volume of fluid (VOF) methods. This method has acceptable accuracy for tracking the position and deformation of the free surface. In this study, an unsteady, two-dimensional, and laminar fluid flow regime is considered. The effect of immersion depth, Froude number, fluid velocity, direction of rotation of the cylinder, and reduced velocity variation on the behaviour of the free surface, forces, heat transfer, and vibration response of the cylinder have been investigated. The results for the stationary cylinder showed that the deformation of the free surface increases with the increase of the Froude number. Also, different patterns of vortex formation were observed in the investigated areas. This change in the cross-flow pattern affects the amount and amplitudes of investigated parameters. For the rotating cylinder, it can be seen that for counter-clockwise rotation, the drag coefficient decreases with increasing rotation velocity, and for clockwise rotation, the drag coefficient increases with increasing rotation velocity