A conceptual stochastic model is developed that describes the natural spatial variability of nonreactive solute concentrations in large groundwater systems. The spatial variation in aqueous concentration is associated with dissolution from source areas of high mineral enrichment in the aquifer matrix. The stochastic model considers randomly varying inputs of a solute species from source deposits that occur as a two‐dimensional spatial Poisson process. A steady state advective‐dispersive transport equation is utilized to predict the downgradient movement of the solute from the source areas. The total groundwater concentration at any location is calculated from the superposition of the individual contributions from each source area in the aquifer. A spatially varying concentration field results, described mathematically by a filtered Poisson process model. The theoretical concentration field is nonstationary, with the mean and variance increasing, and the coefficient of variation decreasing, in the direction of groundwater flow. Gaussian fields for abundant elements and highly skewed probability distributions for trace elements are indicated by the filtered Poisson process model. Evaluation of elemental concentration data from the Sherwood aquifer in England demonstrates how field data may be analyzed in the context of the stochastic model.