The results of the dynamic modeling of the process, that formed the dust tail of comet C/2012 S1 (ISON), are presented. The images of the comet were acquired with the 1-meter Zeiss-1000 telescope of the Special Astrophysical Observatory of the Russian Academy of Sciences (SAO RAS). To construct the model of the dust tail, the trajectories of 50 million dust particles were traced. The distribution of brightness in the dust tail of the comet was reproduced in the model. According to our model investigations, the observed tail could be formed by dust particles with the sizes ranging from 0.5 to 16.6 µm and the escape velocities from 17 to 130 m/s; the power exponent of the distribution by radius is–2.5, and the maximum age of the dust particles having formed the cometary tail is 25 days. In the paper, the brightness of the comet at the moment of observations is also estimated, and the morphology of the cometary coma is analyzed with the use of digital filters.