The roll dynamics of a Floating, Production, Storage and Offloading (FPSO) hull are of special interest in the present offshore industry. The FPSOs, while on duty need to be stationary for long periods of time in order to enable smooth drilling and oil transfer to the shuttle tankers. The present research is aimed at providing insights into the effectiveness of using anti-roll appendages, like bilge keels, in mitigating roll motion of FPSOs operating in mid-seas. Numerical modeling is a tool that can be extensively used to simulate and investigate real ship motions. The present work details a 2D unsteady Boundary Element Method and Navier-Stokes solver based on Finite Volume Method and their application to modeling roll motions of an FPSO hull. The Navier Stokes solver is a viscous solver and is advantageous when compared to the traditional potential flow solvers due to its ability to capture the effects of viscosity and separation past the bilge keel on the motion of the hull.The method could be applied to three dimensional hulls by using either strip theory or by including the third dimension in the formulation.