Stable isotope data for dissolved carbonate, sulfate, and sulfide are combined with water composition data to construct geochemical reaction models along eight flow paths in the Madison aquifer in parts of Wyoming, Montana, and South Dakota. The sulfur isotope data are treated as an isotope dilution problem, whereas the carbon isotope data are treated as Rayleigh distillations. All reaction models reproduce the observed chemical and carbon and sulfur isotopic composition of the final waters and are partially validated by predicting the observed carbon and sulfur isotopic compositions of dolomite and anhydrite from the Madison Limestone. The geochemical reaction models indicate that the dominant groundwater reaction in the Madison aquifer is dedolomitization (calcite precipitation and dolomite dissolution driven by anhydrite dissolution). Sulfate reduction, [Ca²⁺ + Mg²⁺]/Na⁺ cation exchange, and halite dissolution are locally important, particularly in central Montana. The groundwater system is treated as closed to CO₂ gas from external sources such as the soil zone or cross‐formational leakage but open to CO₂ from oxidation of organic matter coupled with sulfate reduction and other redox processes occurring within the aquifer. The computed mineral mass transfers and modeled sulfur isotopic composition of Madison anhydrites are mapped throughout the study area. Carbon 14 groundwater ages, adjusted for the modeled carbon mass transfer, range from modern to about 23,000 years B.P. and indicate flow velocities of 7–87 ft/yr (2.1–26.5 m/yr). Most horizontal hydraulic conductivities calculated from Darcy's Law using the average ¹⁴C flow velocities are within a factor of 5 of those based on digital simulation. The calculated mineral mass transfer and adjusted ¹⁴C groundwater ages permit determination of apparent rates of reaction in the aquifer. The apparent rate of organic matter oxidation is typically 0.12 μmol/L/yr. Sulfate and, to a lesser extent, ferric iron are the predominant electron acceptors. The (kinetic) biochemical fractionation of ³⁴S between sulfate and hydrogen sulfide is approximately −44‰ at 25°C, with a temperature variation of −0.4‰ per °C. The rates of precipitation of calcite and dissolution of dolomite and anhydrite typically are 0.59, 0.24, and 0.95 μmol/L/yr, respectively. This paper is not subject to U.S. copyright. Published in 1990 by the American Geophysical Union.