The Gorleben salt dome, in the northeastern part of Lower Saxony in Germany, is under investigation as a candidate site for the final disposal of radioactive waste. The diapir is crossed by an Elsterian subglacial erosion channel, which forms the lowermost aquifer and is partly in contact with the cap rock or the salt itself. Saturated brines occur in these areas. The high saline water is overlain by a narrow transition zone in which water salinities decrease to that of brackish or fresh water. Numerical models were constructed to study the behaviour of this variable density groundwater system starting 10 000 years ago at the end of the last ice age. Different combinations of initial conditions and hydrogeological setting may yield similar density distributions. A few of the calculated present density distributions compare well with measured field data. A unique solution to the inverse problem is not yet possible.