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 influence of various environmental parameters on model output was evaluated by sensitivity analysis. Time-integrated water and sediment concentrations and maximum sediment concentrations may be predicted for all rivers on the basis of the river volumetric flow rate only. Maximum concentration in water is, however, also dependent on other river characteristics. For this latter case, generalised modelling approaches are tested for use in situations where detailed hydrological and dispersion data are not available.