Assessing the volume of soil requiring remediation and the accuracy of this assessment constitutes an essential step in polluted site management. If this remediation volume is not properly assessed, misclassification may lead both to environmental risks (polluted soils may not be remediated) and financial risks (unexpected discovery of polluted soils may generate additional remediation costs). To minimize such risks, this paper proposes a geostatistical methodology based on stochastic simulations that allows the remediation volume and the uncertainty to be assessed using investigation data. The methodology thoroughly reproduces the conditions in which the soils are classified and extracted at the remediation stage. The validity of the approach is tested by applying it on the data collected during the investigation phase of a former lead smelting works and by comparing the results with the volume that has actually been remediated. This real remediated volume was composed of all the remediation units that were classified as polluted after systematic sampling and analysis during clean-up stage. The volume estimated from the 75 samples collected during site investigation slightly overestimates (5.3% relative error) the remediated volume deduced from 212 remediation units. Furthermore, the real volume falls within the range of uncertainty predicted using the proposed methodology.