In this study the optimal extraction of lignin and solvent distribution in a multistage cross current extraction cascade system is treated for the solution of constrained non-linear maximization problem. The objective was to simultaneously minimize the solvent loss and maximize solvent convergence in a finite cascade of extractors. Different possible loops are calculated through iterative dynamic programming, and the loops are restricted to certain objective functions. An analytical solution is developed which enables the amount of the make-up solvent to be chosen such that the total profit is maximized. The tabular results are represented on a general graph, giving the optimal combination and number of stages for different solvent distribution conditions. © Published under licence by IOP Publishing Ltd.