Isotropic and transversely isotropic elasto-viscoplastic models are proposed to describe the hysteresis loops of stress-strain relation of blood vessels under cyclic loading. It is assumed that the hysteresis loop is expressed as the sum of the elastic deformation and viscoplastic deformation. On the basis of a finite deformation theory, the elastic part is established by postulating a strain energy density function of the exponential type, while the viscoplastic part is formulated by modifying a viscoplastic model for metals. Comparisons of the numerical results with the literature show that the present models can describe the mechanical behavior of the blood vessels well.