INTRAVAL was set up as an international project concerned with the use of mathematical models for predicting the potential transport of radioactive substances in the geosphere. Such models are used to help assess the long-term safety of radioactive waste disposal systems. The INTRAVAL project was established by the Swedish Nuclear Power Inspectorate to evaluate the validity of these models. Results from a set of selected laboratory and field experiments as well as studies of occurrences of radioactive substances in nature (natural analogues) were compared in a systematic way with model predictions. Discrepancies between observations and predictions were discussed and analysed.