The thermal neutron absorption cross section of a small geological sample weighing about 100 grams can be derived from reactivity measurements within a nuclear reactor. The reactivity method has been used previously to measure the absorption in sandstone samples. Extension of the technique to carbonates requires a more accurate model of the reactor’s response to the sample’s nuclear scattering properties. Such a model has been developed for, the Advanced Reactivity Measurement Facility (ARMF) at the Idaho National Engineering Laboratory (INEL). This model is used to derive the thermal absorption cross section in selected samples of some common geological materials including Ottawa sand, Carthage marble, Austin limestone, and Indiana limestone. The effects of experimental uncertainties, such as reactor temperature, sample position, and imperfections in the reactor model are analyzed with respect to their impact on the accuracy of the absorption cross section measurement.