Abstract: In the process of isotope separation in cascade, some separation working fluids will have chemical reactions in the cascade, and a small amount of solid materials will be continuously produced and deposited in the separation equipment. With the increase of sediment, the separation performance of separation equipment will be gradually affected, and then the production and operation of cascade will be affected. Therefore, the sediment needs to be cleaned regularly. In this paper, a numerical method is proposed to calculate the distribution of different gaseous substances in the cascade. On the premise that the cleaning parameters of a single machine are known, the linear iterative algorithm is used to describe the distribution of various gaseous substances in the cascade based on the mass conservation between cascade stages, and the calculation convergence is achieved through the total mass conservation. The results of the numerical example show that the algorithm can converge stably under different cascade regimes.