Delivery of therapeutic-laden biomaterials to the epicardial surface of the heart presents a promising method of treating a variety of diseased conditions by offering targeted, localized release with limited systemic recirculation and enhanced myocardial tissue uptake. A vast range of biomaterials and therapeutic agents using this approach been investigated. However, the fundamental factors that govern transport of the drug molecules from the biomaterials to the tissue are not well understood. Here, the transport of a drug analog from a biomaterial reservoir to the epicardial surface is characterized using experimental techniques and microscale modeling. Using the experimentally determined parameters, a multiscale model of transport is developed. The model is then used to study the effect of important design parameters such as loading conditions, biomaterial geometry, and orientation relative to the cardiac fibers on drug delivery to the myocardium. The simulations highlight the significance of the cardiac fiber anisotropy as a crucial factor in governing drug distribution on the epicardial surface and limiting factor for penetration into the myocardium. The multiscale model can be useful for rapid iteration of different device concepts and for determination of designs for epicardial drug delivery that may be optimal and most promising for the ultimate therapeutic goal.