A 2‐dimensional vertical section model has been developed to simulate the groundwater head distribution in three major aquifers of the Amadeus Basin, central Australia. The resulting model‐derived velocity profile indicates groundwater flow times along a 250 km long and 6000 m deep section to be several million years. The slow and uneven groundwater flow times in this arid basin result from structural and palaeo‐recharge influences. A simulation of previous wetter conditions confirms these influences and suggests that the present‐day system reflects palaeo‐recharge conditions pertaining to the early Tertiary period, at 50 Ma.