A numerical study is made of flow and mass transfer characteristics for a cup-like cylinder, which rotates steadily about its own central longitudinal axis. This study simulates the earlier mass transfer experiment of Sparrow and Chaboki, which provided only the averaged value of Sherwood number. Comprehensive numerical solutions have been obtained to the Navier-Stokes equations over an extended range of Reynolds number. Numerically-constructed flow visualizations exhibit the structures of three-component velocity and concentration fields. The patterns of meridional flows, which are directly responsible for convective transport, are analyzed. The distributions of azimuthal flow are illustrated. Plots of the local Sherwood number at the inner surface of the cup are given. Physically plausible descriptions are presented of the local mass transfer characteristics for both cases of a transferring base endwall and a non-transferring base endwall. The numerical results of the cavity-average Sherwood number are consistent with the previous experimental data.