This study examines the influence of constitutive models and their parameters on predictions of the spatial and temporal distribution of a finite release of a dense, nonaqueous phase liquid (DNAPL) into a two-dimensional, spatially correlated random permeability field. The base case simulation employed a comprehensive constitutive model that was validated against relevant one-dimensional laboratory experiments. The base case was perturbed in the course of nine individual simulations, where each simulation examined the consequences of simplifying a single model characteristic. None of the nine subsequent simulations was able to reproduce, within ¿10%, the spatial and temporal migration characteristics of the nonwetting fluid body at late time predicted by the base case. Capillary pressure-saturation relationships that do not incorporate specific displacement and terminal pressures are demonstrated to severely overpredict the spatial extent of nonwetting fluid advancement. This suggests that van Genuchten-based models may not be suitable for predicting DNAPL migration in saturated porous media. Not accounting for any one of hysteresis, nonwetting phase trapping, or the proper curvature or end-point values of the nonwetting phase imbibition relative permeability curve profoundly influenced the time predicted for all nonwetting fluid movement to cease. The practical implication of this study is that an appropriate, comprehensive constitutive model, characterized with suitable parameter values, is necessary to accurately simulate a complete DNAPL release below the water table in both space and time.