The paper presents a three cells flotation machine with a specific structure of connections of individual cells and the methods of selecting their parameters. The proposed circuit of the three cells flotation machine is characterized by a different connection structure and the specific parameters of each cell than the serial (cell-to-cell) flotation machine. Defined structure of connections between the cells and proper selection of their parameters ensures the maximum slope of the "separation characteristics" of the machine for the velocity coefficient k. Conducting the process of mineral enrichment in the proposed system enables the most efficient separation of the useful feed components. The research was carried out using numerical methods, where the basis of the study was an analytical description of the connection system of three flotation cells being in a steady state, the distribution density characteristic of the particles flotability and the distribution of ash content. The distribution density function of the particles flotability was determined on the basis of the kinetics of the release of the mass of feed components in the batch flotation process. Based on previous work, the authors have shown that the heterogeneity of the feed is well characterized by the model of the triangular distribution function f(k). Using the distribution of particles flotability, the distribution of ash content was determined in relation to the changes in the flotation velocity coefficient. In the final stage of the study, the effects of enrichment obtained in the three cells serial flotation machine (the most common industrial structure) were compared with those obtained in the three cells flotation machine circuit proposed by the authors.