This paper reconstructs, for the first time, the motion dynamics of an eruptive cloud formed during the catastrophic eruption of the Sheveluch volcano in November 1964 (Volcanic Explosivity Index 4+). This became possible due to the public availability of atmospheric reanalysis data from the ERA-40 archive of the European Center for Medium-Range Weather Forecasts (ECMWF) and the development of numerical modeling of volcanic ash cloud propagation. The simulation of the eruptive cloud motion process, which was carried out using the FALL3D and PUFF models, made it possible to clarify the sequence of events of this eruption (destruction of extrusive domes in the crater and the formation of an eruptive column and pyroclastic flows), which lasted only 1 h 12 min. During the eruption, the ash cloud consisted of two parts: the main eruptive cloud that rose up to 15,000 m above sea level (a.s.l.), and the co-ignimbrite cloud that formed above the moving pyroclastic flows. The ashfall in Ust-Kamchatsk (Kamchatka) first occurred out of the eruptive cloud moving at a higher speed, then out of the co-ignimbrite cloud. In Nikolskoye (Bering Island, Commander Islands), ash fell only out of the co-ignimbrite cloud. Under the turbulent diffusion, the forefront of the main eruptive cloud rose slowly in the atmosphere and reached 16,500 m a.s.l. by 04:07 UTC on November 12. Three days after the eruption began, the eruptive cloud stretched for 3000 km over the territories of the countries of Russia, Canada, the USA, Mexico, and over both the Bering Sea and the Pacific Ocean. It is assumed that the well-known long-term decrease in the solar radiation intensity in the northern latitudes from 1963–1966, which was established according to the world remote sensing data, was associated with the spread of aerosol clouds formed not only by the Agung volcano, but those formed during the 1964 Sheveluch volcano catastrophic eruption