The study of roll damping is investigated for a Floating Production Storage and Offloanding (FPSO). For this purpose, a roll decay test of FPSO is simulated by means of the numerical solution of the slightly compressible Navier- Stokes equations in 2D. The governing equations are solved using the finite volume method and the upwind TVD scheme of Roe- Sweby. The roll damping for rectangular hulls is dominated by viscous effects. Strong vortices are formed around the bilge keel. Hence, in this zone, there is a discontinuity of pressure that the TVD scheme will resolve and capture the physics of the phenomenon without spurious oscillations. The numerical results are compared with experimental data for validating the numerical scheme implemented. Copyright © 2012 by ASMEp.