A mathematical model is developed for the mixing of meteoric and original formation waters in homogeneous aquifers. The theoretical analysis indicates that geologic formations that have had a few to a few tens of pore volumes of meteoric water pass through them may be at steady state with respect to further displacement of their contained fluids. Depending on constraints in the recharge area, the steady state may vary from near meteoric water throughout the whole formation to a spatial variation in concentration ranging from meteoric water in the recharge areas to highly concentrated water at the discharge ends of the system. The former condition is attained when the recharge area incorporates the total depth and breadth of the formation. Where this condition is not satisfied, the concentrations that evolve are controlled by the original concentration of the formation water, the composition of recharging meteoric water, the dispersion parameters, and the size of the recharge area in comparison to the total breadth of the formation as measured along its strike. For heterogeneous formations, the concentration patterns that evolve seem to depend further on contrasts in hydraulic conductivity. This is demonstrated in the Milk River sandstone, which is characterized by several extensive zones of dilute water within narrow, high-conductivity pathways and marked increases in concentration in adjacent, lower-permeability rock. In parts of the aquifer where higher-permeability pathways appear to be absent, the isochlores form a broad linear band with a marked increase in concentration in the flow direction.