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. The IEL was modeled as an impermeable barrier to both water and solute except for the fenestral pores that were assumed to be uniformly distributed over the IEL. The media was modeled as a heterogeneous medium composed of an array of smooth muscle cells (SMCs) imbedded in a continuous porous medium representing the interstitial proteoglycan and collagen fiber matrix. Results for ATP and 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 SMC surface reaction. The ATP concentration distribution depends strongly on the IEL pore structure because ATP fluid phase transport is dominated by diffusion emanating from the fenestral pores. On the other hand, LDL fluid phase transport is only weakly dependent on the IEL pore structure because convection spreads LDL laterally over very short distances into the media. In addition we observe that transport of LDL to SMC surfaces is likely to be limited by the fluid phase (surface concentration less that bulk concentration), whereas ATP transport is limited by reaction on the SMC surface (surface concentration equals bulk concentration).