Abstract: A mathematical model was established for multicomponent separation cascades with losses of working substances in the feed flows, enriched flows and depleted flows of cascade stages. A numerical calculation method to solve the cascade equation was presented. Analytical solution to the cascade equation was obtained in the case of quasi-ideal cascades, that is, the cascades with a constant partial cut at all stages. Formulas were given for the calculation of the relative product and waste flows, the total substance flow, and the component concentrations in the product and waste flows of a quasi-ideal cascade with losses.