Abstract The main objectives of this work are to model the separation of lactic acid from an aqueous mixture by adsorption on a polyvinylpyridine resin (Reillex® 425), and to model the desorption of adsorbed lactic acid with methanol. The adsorption equilibrium isotherm of lactic acid in aqueous mixtures in Reillex® 425 has been measured. A theoretical model describing the column adsorption dynamics of lactic acid from an aqueous solution and its desorption with methanol has been developed and validated with experimental data. The model has been employed to design and optimize a simulated moving bed (SMB) process for recovering lactic acid from a lactic acid/water mixture containing 5% w/w of lactic acid, using the triangle theory and the separation volume method. The simulation results show that it is possible to obtain concentrated lactic acid (80% in water) with high recovery (95%) from lactic acid/water mixtures by SMB. The feasibility of recovering methanol from the extract and raffinate streams of the designed SMB process by distillation has also been analysed.