The theory of multicomponent isotope separation cascade with losses is developed. The losses from each stage of a cascade are set proportional to the how entering the stage, the fraction of flow lost per stage being constant. The interstage flows of each component are expressed as simultaneous linear equations and solved explicitly in the case where the separation factors do not vary from stage to stage. An illustrative example dealing with the separation of the 5-component tungsten isotope mixture in the matched abundance ratio cascade composed of gas centrifuges is included.