High-purity sulfur used in nanotechnology, assumes a total impurity content at the level of 1.10(-3)-1.10(-4) wt% and also limiting impurities at the level of 1.10(-7)-1.10(-8) wt%, which include both molecular and heterogenous nanoparticles. The mathematical model for the efficiency of the capture of nanosized particles by the directional crystallization has been developed. The model was verified on the experimental data on the capture of nanosized particles (silver and germanium (30-60 nm)) by the crystallization front of benzene and then it has been used for calculation of sulfur purification process. It is found that the rate of the crystal growth increases, the energy of the particle that is due to the motion of the melt also increases and, consequently, the rate of transition of particles from the melt into the crystal increases too. It is found that as the rate of the crystal growth increases, the distribution coefficient decreases but at the rate greater than 1 cm/h it begins to increase. With an increase in the rate of crystallization, the rate of the transition of particles from the melt to the crystal increases exponentially with a linear increase of the crystallization rate. The calculations showed that the value of the potential of the disjoining pressure is determined by the values of interaction constant and particle size. Since the value of the particle distribution coefficient between the crystal and the melt in the process of the crystal growth differs from unity, crystallization methods can be sufficiently effective for sulfur high purification.