Estimates of the effective vertical hydraulic conductivity of low permeability strata (aquitards) which overlie an aquifer are required when assessing groundwater resources. One approach to estimation is to conduct pumping tests and analyse the drawdowns using classical leaky aquifer theory. However, unreliable parameter values may be deduced since aquitard storage is ignored in classical leaky aquifer pumping test analysis. Analytical solutions which take account of aquitard storage are available, but there are few published examples of their successful application in practical situations. As an alternative, a numerical model based on the same mathematical formulation as the analytical solutions is developed. The numerical model is used to illustrate the flow processes within the aquifer–aquitard system; an important finding is that vertical velocities at the base of an aquitard initially increase rapidly and subsequently decrease to final steady state values. A field pumping test is analysed in detail. Errors in parameter values, which are likely to occur when aquitard storage is ignored, are illustrated.