The transport of a solute by diffusion into a glassy polymer can lead to swelling of the material. For certain types of polymers, a sharp interface is formed between the swollen region and the glassy core. When the density of the swollen material is much smaller than the density of the glass, a significant convective mass-average velocity is generated within the sample. Previous models have neglected the role this convection plays in solute transport and in the proper calculation of the sample dimensions as a function of time. In this paper, we study the contribution of convective terms to the solute transport process, including the motion of the swollen polymer/solution interface. We also compute the eulerian strains that result from the calculated velocity fields and the stresses that would be generated if a linear viscoelastic model is used as a constitutive equation relating the stress to the strain. We show that serious errors can be generated in the calculations if convective terms are neglected. Furthermore, a comparison of the strains and stresses acting on the polymer with those acting on the mixture of solute and polymer shows that they can be significantly different. The stresses and strains acting on the polymer alone offer the most rational physical picture of the material deformation.