In this study, virtual planar-motion-mechanism (PMM) tests in pure sway motion at constant forward speed are carried out to determine the sway added mass values of a 6:1 prolate spheroid. Added mass values are obtained by solving the Euler equations and the Reynolds Averaged Navier-Stokes (RANS) equations across a range of frequencies and depths. The effect that distance from the surface and radiation waves have on frequency-dependent added mass is evaluated. In addition, the effect of forward speed and viscosity on added mass is studied. While this work focuses on a simple prolate spheroid, the results provide a foundational understanding of the effect that submerged depth has on dynamics of a more geometrically complex underwater vehicle operating near the surface.