Patients with atherosclerosis experience plaque buildup in the coronary artery, reducing blood flow and increasing the likelihood of a blood clot. Balloon angioplasty and the implantation of a metal stent are physical mechanisms that have been used to treat atherosclerosis and the associated stenosis of the coronary artery with some success; however, restenosis occurs in a substantial amount of patients. Most recently, biodegradable drug eluting stents have been shown to significantly lower restenosis rates, where an implanted stent is coated with biodegradable polymer and an immunosuppressant therapeutic drug; however, many parameters have yet to be optimized in this method of treatment. This project considers a stent coated with the biodegradable polymer poly lactic-coglycolic acid (PLGA) and immunosuppressant sirolimus (also known as rapamycin), for circular and square geometries, and half and full extents of embedment. A mass transport simulation in COMSOL 5.1 Multiphysics was used to quantitatively simulate this process with the objective of optimizing these design options with respect to drug delivery. Further, this project aimed to suggest potential improvement to current stent designs. Our model showed that the fully embedded stent resulted a significantly higher concentration profile over a 50-day period for both geometries. Likewise, the square model resulted in a slightly preferred elution profile than the circular model for both extents of embedment. The major limitation of the half-embedded model was loss of drug to the bloodstream; hence, we propose two models for improvement: (1) creating an impermeable membrane at the coating-bloodstream interface, and (2) exclusively coating the half of the stent that is in contact with the arterial wall. Design 1 resulted in a significantly increased spatially averaged concentration profile in the arterial wall at all time points in comparison with the benchmark model, and design 2 showed similar profile to the benchmark, despite containing half the mass of drug.