Erosion and redeposition of sputtered material from a limiter and divertor were analyzed using the REDEP computer code. Both low- and high-Z materials were examined for a wide range of plasma edge temperatures. Redeposition rates are high in most cases, and net erosion rates are predicted to be much smaller than the gross rates. The limiter front face and the entire divertor plate have similar erosion properties. The lifetime of both surfaces depends critically on the redeposition process; under certain conditions relatively long lifetimes may be obtainable.