The unconfined alluvial aquifer at Louisville, Kentucky, is an important source of water for domestic and industrial uses. It has been the object of several modeling studies in the past, particularly via the application of classical analytical solutions, and numerical solutions (finite differences and finite elements). A new modeling procedure of the Louisville aquifer is presented based on a modification of Adomian's Decomposition Method (ADM) to handle irregularly shaped boundaries. The new approach offers the simplicity, stability, and spatial continuity of analytical solutions, in addition to the ability to handle irregular boundaries typical of numerical solutions. It reduces to the application of a simple set of algebraic equations to various segments of the aquifer. The calculated head contours appear in reasonably agreement with those of previous studies, as well as with those from measured head values from the U.S. Geological Survey field measurement program. A statistical comparison of the error standard deviation is within the same range as that reported in previous studies that used complex numerical solutions. The present methodology could be easily implemented in other aquifers when preliminary results are needed, or when scarce hydrogeologic information is available. Advantages include a simple approach for preliminary groundwater modeling; an analytic description of hydraulic heads, gradients, fluxes, and flow rates; state variables are described continuously over the spatial domain; complications from stability and numerical roundoff are minimized; there is no need for a numerical grid or the handling of large sparse matrices; there is no need to use specialized groundwater software, because all calculations may be done with standard mathematics or spreadsheet programs. Nonlinearity, the effect of higher order terms, and transient simulations could be included if desired.