The authors suggest a model of transfer of radionuclides in a river system, which relies on the principle of the chamber model, for the case of hydraulically stationary and chemically equilibrium conditions of interaction of radionuclides in the systems “water–suspensions” and “water–bottom sediments.” The model is based on analytical solutions of a system of equations for different conditions of ingress of radioactive contaminants into the river system: in the inlet cross section; with fallout of radiactive aerosols on the water surface; with ingress of radionuclides with surface flow from a contaminated water catchment. The model is verified using the data of radiation monitoring carried out on an experimental water catchment of the Iput river.