The effects of mechanical properties and chemical affinities of materials on the transport of solutes were studied. Simulations show that the kinetics of permeant fluids in matrices depends on the rheological and chemical properties of the polymer. Fick's law failed to describe transport through viscoelastic materials because of the force exerted on the incoming fluid causing a delay. Reversible binding to immobilizing sites also retarded permeation of molecules. An integro-differential equation was applied to model transport in the presence of solute membrane interactions. While the differential part of the equation was represented by an elliptic operator, the integral part, composed of two integrals, described the contributions of stress and reversible binding. Using Laplace transforms, the steady-state flux and effective time constant were calculated. The latter parameter represents a statistical interpretation of the waiting time to achieve equilibrium in the system. The lag time, that defines the first moment when a detectable concentration is measured in a receiver cell, was also studied using multiple integration. Subsequent analyses revealed the dependence of the steadystate flux, the effective time constant, the lag time on the Young modulus, the viscosity and the binding/unbinding rates. The results presented in this paper make it possible to tune the mechanical and chemical properties to achieve a desired transport profile.