A new computer model to predict catchments and time-of-travel zones to boreholes is described. It takes account of spatially varying recharge which is not included in the most commonly used analytical solution. The model can also accommodate four arrangements of aquifer boundaries, two of which represent strip aquifers while the other two are rectangular. The bases of the model are new analytical solutions for the velocity components due to both recharge and pumping from boreholes. Boreholes in rectangular aquifers are modelled by the method of images. Examples show that taking account of recharge and boundaries gives significantly different results for catchment sizes and shapes from the analytical solution commonly used. The size of time-of-travel zones can be significantly smaller when recharge is taken into account. The main uses of the model will be in reconnaissance and sensitivity studies.