Drug-eluting stents are cardiovascular stents able to release a medical drug after implantation. The medical drug is, in general, aimed at healing the vascular tissues injured after implantation and to prevent restenosis. In spite of their apparent simplicity, drug-eluting stents are very complex medical devices whose development involves the design of complex geometrical shapes, the study of advanced biocompatible materials, and the management of complex pharmacokinetic processes. In this study, we focus on a specific design aspect of the drug-eluting stents. In particular, we analyze the drug-release dynamics from the stent coating, where the drug is initially cast, to the arterial wall surrounding the stent. The aim of this work is to show how mathematical models and numerical simulations can help to identify the desired physical properties of the stent coating in order to ensure a desired drug-release rate.