A mathematical model of the biodegradation processes occurring during remediation of contaminated soils by soil vapor extraction (SVE) is presented. The model includes Monod kinetics for biodegradation and rate-limited mass transfer between the aqueous and the gas phases. These mass transfer limitations appear to explain the major features observed in field results presented in the literature : zero-order kinetics with respect to biomass and contaminant, and a very important increase in the percentage contribution of biodegradation to cleanup with decreasing gas flux. Microcomputer runs with the "exact" algorithm are very time-consuming so faster algorithms have been developed using several approximations. These result in savings of more than 95% in computation time, with errors due to the approximations of less than 1%.