This paper presents the development and demonstration of a two‐dimensional finite‐element hydrogeochemical transport model, HYDROGEOCHEM, for simulating transport of reactive multispecies solutes. The model is designed for application to heterogeneous, anisotropic, saturated‐unsaturated media under transient or steady state flow conditions. It simulates the chemical processes of complexation, dissolution‐precipitation, adsorption‐desorption, ion exchange, redox, and acid‐base reaction, simultaneously. A set of four example problems are presented. The examples illustrate the model's ability to simulate a variety of reactive transport problems. Important results presented include a depiction of the propagation of multiple precipitation‐dissolution fronts, a display of the large errors in model response if the number of iterations between the hydrologic transport and chemical equilibrium modules is limited to one, an illustration of the development of greater concentration of contaminants In groundwater away from a waste site than near the source, and a demonstration of the variation in distribution coefficients of more than 6 orders of magnitude.