This paper describes a mathematical model and an algorithm which can be used for simulation of interlinked column systems consisting of liquid-liquid extraction and distillation. This algorithm is based upon Newton-Raphson iteration technique using suitable damping factors and solutions of a simplified version of model as initial values of exact calculations. With the exception of principlal specifications it is possible to exchange the iteration variables and/or noniteration variables with the design variables to meet requirements of design. A process of recovery of phenol from waste water is illustrated to verify the model and algorithm.