The internal elastic lamina (IEL) which separates the arterial intima from the media affects macromolecular transport across the medial layer. In the present study we have developed a two-dimensional numerical simulation model to resolve the influence of the IEL on convective-diffusive transport of macromolecules in the media. The model considers interstitial flow in the medial layer that has a complex entrance condition due to the presence of leaky fenestral pores in the IEL. Results for Low density lipoprotein (LDL) demonstrate a range of interesting features of molecular transport and uptake in the media that are determined by considering the balance among convection, diffusion and smooth muscle cell (SMC) surface reaction.