A numerical method is presented for cascade analysis and design for multi-component isotope separations. A fundamental issue of interest in cascade analysis and design is the solution of the nonlinear algebraic equation system. This system describes the mass conservation and the separation property of a cascade, which provides the hydraulic state and the component distributions in the cascade. Analytical solutions for the system are only available in a few special cases. Numerical methods are preferred for many of the complicated separation situations; however, the solution process in a numerical method is carried out through iterations and is very sensitive to initial values, which often leads to the failure of the method. Continuation techniques satisfactorily resolve the problem of sensitivity. This paper presents computer algorithms in detail to show how the techniques were implemented in order to tackle the problems in constructing different cascades. Various cascades were employed as test problems, including the well-known matched-R cascade, the quasi-ideal cascade, the less-known matched-X cascade and a newly invented pseudo-binary cascade. Numerical experiments on these cascades demonstrated that these cascades are readily solved with the required properties and that the proposed method is a powerful technique for analyzing and designing isotope separation cascades. (C) 2013 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.