A new tool for the design of multicomponent distillation columns is presented, which is based on analytical solutions of a suitable mathematical model. The assumptions on which ii; is built are (il a large number of stages, which makes it possible to apply a continuous description of the column instead of the usual stage-by-stage equations; (ii) constant molar overflow; (iii) constant relative volatility; and (iv) attaininent of vapor-liquid equilibrium everywhere along the column. The resulting model equations are solved in the frame of Equilibrium Theory, which was originally developed to describe chromatographic processes. Through this approach explicit results may be obtained and both the steady state and the dynamic behavior of high-purity columns can be analyzed. In particular, this work focuses on thr! former, thus obtaining the following results : (i) a complete picture of the different separation regions in the operating parameter plane spanned by the flow-rate ratios in the rectifying and stripping section; (ii) the evaluation of the optimal operating conditions corresponding to each different separation regime, together with the proof that these are equivalent to the Underwood minimum reflux conditions; (iii) the explanation of well-known features of multicomponent distillation such as pinch conditions and nonlinear behavior. Numerical examples of binary and multicomponent separations are presented and discussed.