The need of reliably solving systems of nonlinear equations often arises in the everyday practice of chemical engineering. It? general, standard methods cannot provide theoretical guarantee for convergence to a solution, cannot reliably find multiple solutions, and cannot prove nonexistence of solutions. Interval methods provide tools to overcome these problems, thus achieving reliability. To the authors' best knowledge. computation of distillation columns with interval methods have not yet been considered in the literature. This article presents significant enhancements compared with a previously published interval method of the authors. The proposed branch-and-prune algorithm is guaranteed to converge, and is fairly general at the same time. If no solution exists then this information is provided by the method as a result. Power (if the suggested method is demonstrated by solving, with guaranteed convergence, even the MESH equations of a 22 stage extractive distillation column with a ternary mixture. (C) 2009 American Institute of Chemical Engineers AIChE J, 55: 1695-1704, 2009