The novel "multicolumn countercurrent solvent gradient purification" (MCSGP) process has been modeled for the purification of a polypeptide mixture characterized by a strong non-linear competitive adsorption isotherm. As a model system, the purification of an industrial polypeptide mixture containing 46% of the hormone calcitonin has been selected. The many impurities contained in the mixture have been lumped into three key impurities, which are selected as the ones eluting closer to the main component. The simulation model allows for a better understanding of the complex operating behavior of the multicolumn system, which has been experimentally investigated in a previous work. Through a systematic parametric analyses of the model behavior, the main operating parameters controlling the process performance in terms of purity and yield are investigated. The study of internal liquid and adsorbed phase concentration profiles along the unit for the different operating conditions allow elucidating the working principle of the new separation process. It is found that the MCSGP unit achieves much higher yields for a given product purity than the corresponding single-column batch units.