This study examines the interactions between barotropic Rossby waves and a zonal current, with particular reference to the Antarctic Circumpolar Current (ACC). In the high latitude of the Southern Ocean, the effect, which provides the restoring mechanism for Rossby waves, is relatively weak, resulting in barotropic waves that are extremely long, with periods of the order of 1 week or longer. We model the interactions between the current and the waves using the linearized potential vorticity (PV) equation with the inclusion of background PV terms corresponding to a barotropic zonal flow of finite width. An analytical solution is found for the simplest, piecewise-linear flow and numerical solutions obtained for more realistic, smoothly varying flows. The results show that, in general, the long waves are not appreciably modified or reflected by the shear flow, except in the case where the wave is incident at an oblique angle. Wave reflection is also more pronounced for shorter waves, such as Rossby waves having eastward group velocity or the case where the wave frequency is just below the cutoff frequency.