A method is proposed for the simulation of groundwater flow in regional aquifers dissected by dykes of low permeability or by geological faults, which act as barriers to flow and which can have a considerable influence on the available groundwater resources. The method has been verified by a comparison of numerical results with the analytical solution to a test problem. The method has been applied to an area of the Cave Sandstone aquifer in Botswana which has been affected by dyke intrusions which significantly affect its potential for large-scale groundwater development.