The uptake of solutes into plastic infusion and perfusion tubing has been well documented, but the kinetics of the uptake process is not well-defined. Three mathematical models have been developed to describe the outflow fraction concentration--time profiles for solutes sorbed into the plastic tubing during infusion and perfusions. The models are referred to as model 1, convection--diffusion; model 2, convention-- interfacial resistance--diffusion; ad model 3, convection--interfacial resistance--infinite sink models. In each model, plug flow is assumed and, in order to minimize the number of variables required, solutions are limited to early times when the plastic behaves as an infinite sink. Initial conditions of (i) no solution in the tubing and (ii) a preloading of tubing with drug solution are considered for each of the three models. Two parameters, one being the transit time of solution through tubing (tmin) and the other a measure of the affinity and diffusivity of the solute in the plastic (SN), are sufficient to describe the outflow concentration--time profiles for solutes with sorption into tubing being limited by diffusion in the plastic (model 1). A single parameter, which is the effective interfacial permeability coefficient (H), is sufficient to describe the outflow concentration--time profiles for solutes with sorption into tubing being limited by an aqueous--plastic interfacial barrier (model 3). The three parameters (tmin, SN, and H) are required when uptake into tubing is limited by a combination of diffusion into plastic and an interfacial resistance (model 3). Each model has a characteristic outflow concentration--time profile determined by the relative magnitude of diffusivity of the solute in the plastic to that across the interfacial barrier. The sorption of nitroglycerin and isosorbide dinitrate are adequately described by the convection--diffusion model (model 1 (ii)) whereas the convection--interfacial resistance--diffusion model (model 2 (ii)) is required to describe the sorption of diazepam and chlorpromazine.