[en] A computer program, NUMATH (Nuclear Material Holdup Estimator), has been developed to estimate compositions of materials in vessels involved in unit operations and chemical processes. This program has been implemented in a remotely operated nuclear fuel processing plant. NUMATH provides estimates of the steady-state composition of materials residing in process vessels until representative samples can be obtained and chemical analyses can be performed. Since these compositions are used for inventory estimations, the results are determined for the cataloged in container-oriented files. The estimated compositions represent materials collected in applicable vessels - including consideration for materials previously acknowledged in these vessels. The program utilizes process measurements and simple performance models to estimate material holdup and distribution within unit operations. In simulated run-testing, NUMATH typically produced estimates within 5% of the measured inventories for uranium and within 8% of the measured inventories for thorium during steady-state process operation