The authors have investigated the process of asbestos-cement dust slippage past dust collectors with countercurrent swirling flows. They took into account the mass rate of dust getting to the working zone air, the total gas flow rate, the length of the lower inlet branch duct, the conditional relative speed in the midsection of the apparatus, the ratio of the flow rates delivered to the upper and lower inlets, the distance between the axes of local exhausts, the relative concentration and particle size distribution of dust. In the course of the investigation, the methods of mathematical statistics and probabilistic-stochastic approach were applied. The optimal ratio of the given parameters was determined, at which the maximum dust collection efficiency was observed.