This paper discusses the results of calculation of climatic river runoff for the subarctic East Siberia region obtained with a linear reservoir model. For the verification of the model, the measurements data as well as the MERRA reanalysis data for the XXth century were used. For the XXIst century, the calculations with the data of the INM, the CRNM, the GFDL, the HadGEM, the MIROC5, the MPI models of the scenario RCP 8.5 of the Project CMIP5 IPCC were carried out. The results give a remarkable increase of the annual runoff for all the models. The annual variability has the positive trend during the XXIst century.