Abstract: This paper deals with nonlinear elastic properties of large blood vessels. The artery is modeled to be a locally triclinic, transversely isotropic, inco-mpressible,axisymmetric thick-walled tube with large deformation. In order to establish nonlinear constitutive relationship of arterial tissues, a nonlinear strain energy density function, including to the third order strain terms, is proposed for the second order nonlinear stress-strain relationship of the blood vessels. In this function, the coefficient of each term is expressed in Lame's constants. A comparison between the analytical result and available data shows that the nonlinear stress-strain relationship of canine arterial tissues can be quite satisfactorily described by the proposed strain energy density function.