Mathematical models for soil vapor extraction (SVE) are developed which model solution of nonaqueous phase liquid (NAPL) and mass transport of volatile organic compounds (VOCs) through low-permeability lumps, lenticular structures, and discontinuous layers of clay by means of a distributed diffusion approach. The well configurations modeled are that of a single buried horizontal slotted pipe and that of a single vertical well screened along a short length near its bottom. The models yield high off-gas VOC concentrations initially, followed typically by vary rapid drop-offs to relatively long plateaus, followed in turn by terminal tailing, the length of which is highly variable and determined by the thickness of the low-permeability layers from which diffusion is occurring and by the size of the NAPL droplets (if NAPL is present). The results are in agreement with a previous, simpler model; they indicate that it will be impossible to accurately predict SVE cleanup times from data taken in short-term pilot-scale experiments removing only 5-25% of the VOC present in the domain of influence of the well.