The boundary layer of a weakly ionized rare gas discharge is treated using kinetic theory. A self‐consistent two‐scale analysis is performed and the exact presheath and sheath solutions are constructed for the following model: A plasma consisting of Boltzmann distributed electrons and singly charged atomic ions is in contact with a negative absorbing wall. The ion kinetics is dominated by charge exchange with cold neutrals (T0≪T−). The mean‐free‐path &lgr; is constant and large compared with the electron Debye length &lgr;D. This model represents a collision‐dominated counterpart to the well known Tonks–Langmuir model of the collision‐free plasma.