The large epicardial coronary arteries and veins span the surface of heart and gradually penetrate into the myocardium. It has recently shown that the remodeling of the epicardial veins in response to pressure-overload strongly depends on the degree of myocardial support. The non-tethered regions of the vessel wall show significant intimal hyperplasia as compared to the tethered regions. Our hypothesis is that such circumferentially non-uniform structural adaptation in the vessel wall is due to the non-uniform wall stress and strain. The transmural stress and strain are significantly influenced by the support of the surrounding myocardial tissue that significantly limits the distension of the vessel. In this finite-element study, we modeled the non-uniform support by embedding the left anterior descending (LAD) artery into myocardium to different depth, and analyzed the deformation and strain in the vessel wall. The circumferential wall strain was found to be much higher in the untethered region than the tethered region at physiological pressure. Based on the hypothesis that elevated wall strain is the stimulus for remodeling, the simulation results suggest that the large epicardial coronary vessels have higher tendency to become thicker in the absence of myocardial constraint. This study provides a mechanical basis for understanding the local growth and remodeling of vessels subjected to various degrees of surrounding tissue.