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A typical example of viscoelastic matrices is represented by polymeric particles devoted to the controlled release of active agents (drugs) that swell when put in contact with an external solvent, typically a physiological medium. Although, in general, physiological fluids can be considered Newtonian, this is not always the case, let us consider, for example, the mucus present in different organs such lungs when affected by chronic obstructive disease (bacterial infections and cystic fibrosis, for instance). Swelling allows the release of the embedded drug due to the enlargement of the meshes of the polymeric network. The demand for more and more sophisticated drug delivery systems requires to theoretically study in high detail the mass transport phenomena involved in the swelling and release processes. The present study concerns with the mathematical modelling of both transport processes in the case of a viscoelastic matrix swollen by a viscoelastic fluid. While matrix viscoelasticity is accounted for by the generalized Maxwell model, a mean relaxation time accounts for fluid viscoelasticity. The model assumes that solvent uptake gives origin to an internal stress, due the polymeric network reaction to enlargement, able to affect solvent transport and thus, drug release. Despite the complexity connected to the theoretical description of stress and deformation in the swelling matrix, it is generally assumed that the stress state can be approximated by a scalar that can be viewed as an osmotically induced viscoelastic swelling pressure related to the trace of the stress tensor. At the same time, assuming incompressible materials and vanishing deformation gradient inside the matrix, deformation can be simply represented by a scalar quantity (the radial deformation in the case of spheres). Model simulations indicate that the higher the swelling solvent relaxation time, the lower the effect of matrix viscoelastic properties on mass transport phenomena