This research presents the use of analytical and numerical modeling techniques to aid in the characterization of a subsurface contaminant plume associated with a hazardous waste site (HWS). This study presents a discussion of various model types and their governing equations, as well as outlines the specific analytical and numerical models used for the research. The U. S. Geological Survey (USGS) Method of Characteristics (MOC) model is investigated in depth, including an overview of the model, with a description of the code's solution technique and input parameters, and a sensitivity analysis to determine the effect of each parameter on the model's simulation of a subsurface contaminant plume. An abandoned hazardous waste site in Conroe, Texas is employed to illustrate the use of modeling techniques to help evaluate the data base, investigate the hydrogeologic parameters which most influence the contaminant plume migration, and determine new objectives for the ground water monitoring program.