In the present study, the salt-water up coning problem in coastal unconfined aquifers is investigated. The dimensional analysis is used to provide information about the optimum well depth and the optimum pumping rate for a well suggested to be partially penetrating a coastal unconfined aquifer example. The Bear and Todd's method of superimposing the effects of hydrodynamic dispersion on the up coning system, is used to predict the concentration profile with depth below the pumped example well at a workable dispersivity of the aquifer. The results shows that, the concentration of pumped water is still suitable for irrigation under certain conditions. Comparison of the estimated salinity profile for the example well , with the measured salinity profile in a neighboring well drilled in the same area, indicates an order of magnitude agreement. The results encourage the use of the present solution methodology of the up coning pumping system problem as it seems to be extremely useful in the cases where the dispersion measurements are unavailable in the studied aquifer