Many different calculation procedures for the numerical solution of multistage equilibrium separation processes have been proposed. With the exception of the global Newton—Raphson method, disadvantages of which seem to be the enormous requirements for computer memory and the necessity of enumerating of a large matrix of partial derivatives (Jacobian), these methods do not enable solving of problems with various specifications of variables in a simple way. Usually, it is necessary to specify products flowrates and reflux ratio or recovery fraction of the key component, respectively. The problems with different sets of input specifications must be solved by means of indirect methods, which are usually very time-consuming, or cannot be solved at all. Here, the algorithm, based on the Newton—Raphson method, is described. This algorithm is a modification (simplification) of Russell's method and makes it possible to solve the problems with arbitrary specifications of stage temperature, flowrate and/or stage composition. The suitable choice of independent variables (stripping factors and sidestream withdrawal factors) results in a relatively small number of equations enthalpy balances and specification equations) and the Newton—Raphson method can be applied. The algorithm is stable, it converges fairly fast and enables the solving of arbitrary column configurations. Its facilities have been verified by solving of numerous problems especially from the petroleum refining industry.