An application of an inverse flow and transport model to a contaminated aquifer is presented. The objective of the study is to identify physical and nonreactive flow and transport parameters through an optimization approach. The approach can be classified as a statistical procedure, where a flow and transport simulation model is combined with nonlinear least squares multiple regression. The U.S. Geological Survey method of characteristics model is used to simulate flow and transport, and the optimization part is solved using a Levenberg-Marquardt algorithm. The sensitivity of the optimization approach to steady state versus transient flow conditions and to the amount of hydraulic and solute data used is investigated. The flow parameters, transmissivity and leakage factor, are estimated simultaneously with the transport parameters: source strength, porosity, and longitudinal dispersivity. This paper is the first in a two-paper series describing contaminant transport at a waste residue site. In the second paper, reactive transport at the site is investigated.