Non-Body-Of-Revolution (Non-BOR) submarine hulls allow more payload exibility and may yield improved maneuverability. Initial testing with free-running models and wind-tunnel experiments have, however, revealed a noticeably different maneuvering behavior of Non-BOR versus axisymmetric hulls due to the considerably altered hydrodynamics. Therefore, thorough understanding of the relevant flow physics for Non-BOR hulls is critically needed. The combination of three-dimensionality and unsteadiness results in a highly complex time-dependent topology of the separated region, which is not well understood. 3-D direct simulations for the Virginia Tech Non-BOR generic ellipsoid submarine hull were carried out for a case where roll instability was identified in the Virginia Tech experiments. Simulations for a Reynolds number (based on model length) of 20,000, an angle of attack of 30 degrees and a side-slip angle of 22 degrees reveal a highly asymmetric, unsteady lee vortex configuration.