Cardiovascular diseases are a major cause of death in the world and are closely related to the dynamics of the blood and arterial wall mechanics. Not only in the cardiovascular system, but also in the whole body system, the heart is the most important organ that if the blood vessels of it blockage, heart function will impaired. Effective solutions to resolve blockage of coronary is the bypass surgery in which a replacement vessel for the blood supplying to the heart is using. So study the behavior of the vessels that use for the bypass is important. The goal of this study is the investigation of the mechanical behavior of saphenous vein by using the tensile biaxial tests. So eight human saphenous samples obtained and the planar biaxial tests were performed on the tissue specimens by applying simultaneous loads along the circumferential and longitudinal directions. Then the measured data were fitted into the four-parameter Fung-type model and also to the five-parameter Mooney–Rivlin model this could be used in finite element packages for numerical analysis. The specimens were stiffer in the longitudinal than in the circumferential direction. The specimens showed some degree of anisotropy.