MINTRAN is a new model for simulating transport of multiple thermodynamically reacting chemical substances in groundwater systems. It consists of two main modules, a finite element transport module (PLUME2D), and an equilibrium geochemistry module (MINTEQA2). Making use of the local equilibrium assumption, the inherent chemical nonlinearity is confined to the chemical domain. This linearizes the coupling between the physical and chemical processes and leads to a simple and efficient two-step sequential solution algorithm. The advantages of the coupled model include access to the comprehensive geochemical database of MINTEQA2 and the ability to simulate hydrogeological systems with realistic aquifer properties and boundary conditions under complex geochemical conditions. The model is primarily targeted toward groundwater contamination due to acidic mine tailings effluents but is potentially also applicable to the full range of geochemical scenarios covered by MINTEQA2. The model is tested with respect to ion exchange chemistry and with respect to precipitation/dissolution chemistry involving multiple sharp fronts. The companion paper presents two-dimensional simulations of heavy metal transport in an acidic mine tailings environment, focusing on environmental implications. ¿ American Geophysical Union 1994