We examine rimming flows, i.e. flows of a liquid film on the inside of a horizontal rotating cylinder. So far this problem has mostly been explored using the so-called lubrication approximation (LA). It was shown that, if the volume of the liquid in the cylinder exceeds a certain threshold, then a shock similar to a tidal bore appears in the lower half of the cylinder on its rising side. The position of the shock can be characterized by the polar angle theta (s), with a value between theta (s) = -90A degrees (the bottom of the cylinder) and theta (s) = 0A degrees (the horizontal direction). In this study, we examine rimming flows without the LA, by solving numerically the exact Stokes equations. It is shown that a steady solution describing a (smoothed) shock exists only if . Shocks with lower locations overturn, so no steady solution exists. It is also shown that smoothed-shock solutions have an oscillating structure upstream from the shock. If, however, capillary effects are taken into account, the range of theta (s) where solutions overturn contracts, and if surface tension is sufficiently strong, solutions exist for all values of theta (s).