Sorption in glassly polymer accompanied by strong concentration effects, is investigated theoretically. Asymptotic solutions for the concentration profiles are obtained and show that the fronts are very sharp, but advance with a square root of time type of dependence. The system is subdivided into two regions, a swollen gel and dry polymer regions using theories from interfacial phenomena. The dynamics are shown to be stable to small perturbations. The stress effects from swelling are shown to be negligible under this model. © 1988, Taylor & Francis Group, LLC. All rights reserved.