A new Monte Carlo (MC) method for calculating the isotopic inventory of material subjected to a neutron flux is developed and demonstrated. The method is particularly suited to modeling materials that flow through a system in a nondeterministic path. The method has strong analogies to MC neutral particle transport. The analog methodology is fully developed, including considerations for simple, complex, and loop flows, and enabling concepts such as sources and tallies. A wide variety of test problems is employed to demonstrate the validity of the analog method under various flow conditions. The method reproduced the results of the as-low-as-reasonably-achievable deterministic inventory code for comparable problems and is self-consistent when comparing complex flow scenarios to mathematically identical simple flow scenarios. A demonstration of highly scalable parallelization does not eliminate the need to develop variance reduction techniques.