This paper evaluates and generalises state-of-the-art approaches for modelling short duration liquid discharges of radionuclides (3H, 14C, 60Co, 134Cs, 137Cs, 65Zn, 89Sr, 90Sr, 125I, 131I, 241Am, isotopes of Pu and U) to rivers. An advection–dispersion model was parameterised and used to predict the concentrations of radionuclides in the river environment, i.e. in river water, river bed sediment and fish (Part II of this paper covers uptake to fish). The coupled transport and bio-uptake model was used to predict the concentrations of radionuclides in the River Thames, UK, and one of its tributaries as a result of hypothetical short duration discharges. A simplified version of this model was developed and presented as “look-up” graphs. The i...