Intensive volcanic eruptions of an explosive type are accompanied by release of a great amount of ash particles into the atmosphere. These particles are finely dispersed (< 2 mm in size) products of magmatic melt fermentation, and their precipitation on the underlying surface is largely controlled by atmospheric transport. The present work proposes an approach to estimate the total released mass (TRM) of ash at minimal a priori data on dynamics of explosive process, on the basis of, first, direct numerical modeling of atmospheric transport and gravity precipitation of ash particles and, second, field observation data. To exemplify, the case study of the strong explosive eruption of Bezymyanny volcano on December 24, 2006 is considered (TRM > 3.8 Mt, height of eruptive column is 13-15 km above sea level). The results of the model calculations for this event are compared to independent TRM estimates by using standard methods based on the counting of precipitation areas.