For many types of floating structures, roll motion is the most important wave induced motion. More specifically, roll motion is of high significance for barges, in order to correctly predict the acceleration of the structure caused by roll motion and determine the procedure of sea-fastening and off-loading. The correct forecast of roll motion requires accurate estimation of roll damping. At the same time, the main sources of roll damping are the creation of waves, skin friction and creation of vortices (eddies), due to roll motion. For this reason, the physics of the problem cannot be fully described by a flow model based on potential theory, as it is highly dependent on vorticity and viscous effects. As a consequence, potential theory algorithms underestimate roll damping, which results in over prediction of roll motion and thus in a conservative estimate of workability. It is also important to mention that the vorticity and the viscous effects, lead to nonlinear damping characteristics. More specifically, the roll damping moment is controlled by its odd numbered harmonics, the first of which is dominant. Consequently, it is common to express the damping moment in an equivalent linearized form, equal to the first harmonic. During the last years simulating the flow around the rolling vessel using viscous flow algorithms is becoming more and more popular. Using CFD (Computational Fluid Dynamics) is a cheap and fast way to create a “numerical” wave tank and perform numerical decay tests, forced roll simulations, and roll response simulations in regular waves. Of course the underlying algorithm should be validated, before any commercial or scientific use. In this thesis, roll damping will be estimated by performing virtual forced oscillation tests, and the computed roll damping coefficients will be presented as a function of roll amplitude. The virtual forced oscillation tests have been performed with the open-source CFD software OpenFOAM. Additionally, numerous numerical experiments are performed in order to choose the optimum discretization schemes, turbulence model, mesh and time configurations. Finally, Ikeda’s experimental data is used in order to validate the viscous flow algorithm and the numerical model. Two methodologies have been used in order to determine the nonlinear roll damping. In the first case the free surface is included in the viscous flow model, using the Volume of Fluid method. The second approach disregards any free surface effect and the total damping is calculated as a superposition of viscous (by viscous flow algorithm) and wave (by potential theory algorithm) damping. Both approaches are compared with Ikeda’s experimental data and it is concluded that both methods are able to capture accurately the linearized roll damping coefficients, for various amplitudes. Finally, viscous flow simulations of the full scale barge, in order to calculate the roll damping coefficients, are notably time consuming. For this reason, in order to reduce the computational time, the methodology which neglects the free surface effect, is chosen, as it is a good compromise between time efficiency and accuracy.