Alluvial aquifers can often supply large quantities of water but if they are overlain by a low permeability zone, the recharge may be restricted with the result that the long term safe yield of the aquifer is greatly reduced. This paper describes a study of an alluvial aquifer in Bangladesh where there is a low permeability layer overlying the main aquifer. Pumping tests carried out in this aquifer were analysed using a numerical model which represents both the main aquifer and the overlying low permeability zone. Using the aquifer parameters deduced from the pumping test analysis, the numerical model was then used to represent five years of pumping. This long term simulation indicated that there would be a serious decline in the pumped levels and that a water table would develop in the main aquifer and would fall at a rate of almost five metres per year.