This paper describes a numerical technique for analyzing the viscous unsteady flow around oscillating ship hulls. The technique is based on a general Reynolds-averaged Navier-Stokes (RANS) capability, and is intended to generate viscous roll moment data for the incorporation of real-flow effects into potential flow ship motions programs. The approach utilizes the finite analytic technique for discretizing the unsteady RANS equations, and a variety of advanced turbulence models for closure. The calculations presented herein focus on viscous and vortical effects without free-surface, and utilize k-epsilon turbulence modeling. Series variations are presented to study the effects of frequency, amplitude, Reynolds number, and the presence of bilge keels. Moment component breakdown studies are performed in each case to isolate the effects of viscosity, vorticity, and potential flow pressures.