Biodegradation, the transformation of organic matter using microorganisms, is a promising technology for ground water cleanup. The research presented in this dissertation is aimed at developing numerical techniques for simulating biodegradation coupled with physical transport processes in ground water. The focus is mainly on aerobic biodegradation. A two-dimensional biodegradation model, BIOPLUME II, was developed that incorporates two different conceptual approaches for simulating aerobic biodegradation. The first approach assumes that the transport of oxygen into a contaminant plume is limiting and that biodegradation could be approximated with an instantaneous reaction between the contaminants and oxygen. The second approach argues that the biodegradation of organic contaminants is kinetically limited by microbial utilization rates and that the process could be represented with a dual Monod kinetic relationship between oxygen and the contaminants. Comparisons between the instantaneous model and the kinetic model suggest that oxygen transport is limiting in aquifers with seepage velocities less than 0.03 ft/d. The rate of oxygen utilization takes on more importance in aquifers with high velocities and for organic contaminants which are slowly degrading. The instantaneous reaction model is applied to a pilot scale bioremediation demonstration project at the Traverse City field site. A nutrient mix containing phosphate, ammonia and an oxygen source is injected into a portion of the contaminated aquifer. The BIOPLUME II model was used to select the design parameters for the test, mainly: the injection flow rate, the number of injection wells and the time required for renovation. Dissolved oxygen and contamination data from the monitoring wells in the demonstration area for the last ten months of operation were analyzed to assess the degree of cleanup. The field data indicate that benzene, toluene, ethyl benzene, and xylenes have been selectively removed from the soils and water in the demonstration area. The field data were compared to the predictions from the BIOPLUME II model. The model results imply that modeling is a useful tool for predicting the biodegradation of organic contaminants in ground water.