A hydrologic model based on the Analytic Elements Method (AEM) has been developed for a phreatic aquifer in the General Separations Area (GSA), of the Savannah River Site (SRS), South Carolina, USA. The AEM is a semi-analytical method that relies on the superposition of individual closed-form solutions of elements representing the main hydrologic features of a site. Our study adopts techniques from the stochastic subsurface hydrology to assess the impact of precipitation (and consequently infiltration) variations on the flow field. The precipitation was considered as a random variable following a statistical model that was obtained from a record of the past 112 years. A measure of the variability of the hydraulic head field is obtained through Monte Carlo simulations and a discussion on the uncertainty in different regions of the model is provided. The ease of model development and the small processing power required by AEM models, make the method applicable not only to initial investigations for the identification of test parameters and boundary conditions but also as a tool that in a stochastic framework can provide initial estimations of uncertainty associated with certain model assumptions.