A critical issue in long-pulse tokamak discharges is the need for density control and power-handling capability in the presence of wall outgassing, neutral beam injection, and pellet fueling. Direct particle and energy exhaust in Tore Supra is obtained with a system of pump limiters, including six located at the bottom of the machine and a large horizontal module at the outer midplane. This paper focuses on two-dimensional (2-D) modelling of the scrape-off-layer (SOL) and outboard pump limiter, using the MHD fluid code b2 and the neutral transport code DEGAS. Temperature, density, and ion flux data from Langmuir probes in the throat of the limiter are used along with estimates of the power scrape-off-length from infrared camera data to obtain a self-consistent description of the SOL plasma/neutral source distribution within the limiter and throughout the SOL. Good agreement with measured quantities is obtained, and three to four iterations of the b2/DEGAS calculation are necessary for convergence.