Relatively simple compartmental models of transport of radioactive substances by a uniform flow are quite often successfully used for assessment of concentrations of radionuclides in water, bottom sediments and flood plains of rivers. However, one should take into account specificity of contamination of a river to be simulated. In this work the results of modelling of 89,90 Sr, 137 Cs, and 239,240 Pu migration in the Techa River were compared with observed data. As a result of the comparison the authors have supposed that taking into account of the process of mass exchange between the main stream of a river and underflow is important for the adequate modelling of migration and accumulation of radionuclides (and other contaminants with similar physical and chemical properties) in rivers that were polluted during a long period of time. It is known that underflow of a river can reach 30% of the main stream. The performed analysis of comparison of the modelling results with the observed data has enabled an evaluation of numerical values of parameters by means of which the interaction between the main stream and the underflow may be described. The choice of the Techa-river as an example was not casual. For more than 50 years the "Mayak" plant was fulfilling its important defense mission and discharged contaminated effluents to the Techa-river. As a result the whole river and its basin have become contaminated by long-lived radionuclides. The issues of the Techa-river contamination by radionuclides and simulation of their transport have been given attention over decades by many scientists.