---

A new mathematical model for identifying pollution sources in aquifers is presented. The model utilizes Lagrange Constrained Optimization Method (LCOM) and is capable to inversely solve unsteady fluid flow in saturated, heterogeneous, anisotropic confined and/or unconfined aquifers. Throughout the presented model, complete advection-dispersion equation, including the adsorption as well as retardation of contaminant, is considered. The well-known finite element method is used to discretize and solve the governing equations. The model verification is implemented using a hypothetical example. Also, the applicability of the developed code is illustrated by the real field problem of Ramhormoz aquifer in southwestern Iran.