Abstract Based on data from the Chernobyl accident, the ‘Wash-off’ scenario was developed to provide an opportunity to test models intended to simulate the movement of trace contaminants from terrestrial sources to bodies of water. The specific objective of the test was to take into account chemical speciation, its effect on the transfer of contamination from soil to water, and the geochemical and geophysical processes that affect such transfer. Modellers were provided with descriptions of two experimental plots near the Chernobyl Nuclear Power Plant (NPP), one using simulated heavy rain (HR) and one using snowmelt (SM). They were requested to estimate the vertical distribution of total 137Cs and 90Sr and their specific forms in the soil prior to the experiments, concentrations of each radionuclide in surface runoff (separately for particulate and dissolved forms) and the total amount of each radionuclide lost from plot HR during the experiment. All predictions were to be provided as best estimates with 95% subjective confidence intervals about the best estimates. In this paper, a brief description of the modelling results is provided, together with discussions of the performance of individual models in comparison with the actual measurements and of the sources of uncertainty in the model predictions. Our conclusion is that the predictive accuracy of the mathematical models could be improved by (1) improvement of model structure to include all relevant mechanisms; and (2) further use and improvement of methods for estimation of parameter values for the situation being modelled.