In this work, considering that under physiological conditions the arteries are subjected to a large initial static deformation and additional small dynamical displacements are superimposed on this initial field, a Boltzman type of constitutive relation is presented for arterial wall materials. For its simplicity in the analysis, the material under investigation is assumed to be isotropic, incompressible and constitutionally nonlinear in Green deformation tensor but linear in the history of deformation tenser. The numerical values of elastic coefficients are obtained by comparing the analytical results with experiments by Simon ct nl. [Circ. Res. 30, 491-500 (1972)]. For the determination of viscoelastic coefficients we studied the propagation of torsional waves in a prestressed thin cylindrical tube and proposed a method of determining the viscoelastic coefficients. Copyright (C) 1996 Elsevier Science Ltd.