In Germany, geochemical modelling takes a strong position in two aspects of broader public interest. The first aspect is the safety assessment of a nuclear waste repository, the second is remediation of uranium mining areas. In both aspects, the application of geochemical modelling is stipulated by authorities. This situation results from the possibility to model highly complex situations by computers. The increase in computing power experienced in recent times now offers techniques to assess the sensitivity of modelling results to uncertain input data both in the thermodynamic data base and the site-specific field data. Both aspects are investigated by using Monte Carlo methods in combination with non-parametric statistics. A probabilistic geochemical modelling of uranium mill tailings leaching is demonstrated by application of TReaC modelling code using a simplified site model.