[en] Many waste sites (>400) located within the Central Plateau portion of the Hanford Site received liquid discharges during the nuclear weapons material production mission (1944-1988). The Hanford Soil Inventory Model (SIM) is developed to quantitatively evaluate the discharged inventory for important radionuclides and chemicals at a given waste site to support fate and transport modeling of contaminants. An analytic approach was developed to estimate inventory and associated uncertainty. The approach was implemented for SIM and compared to a prior stochastic implementation applying a Monte-Carlo sampling approach. The analytic approach provides exact mean and variance results and the run times are much faster compared to the Monte-Carlo sampling approach. With the improved solution method using the analytical approach, it is feasible to run inventory updates and reduce associated uncertainty ranges. (authors)