<p>We analyze shear stress distributions in an arterial wall and torques with torsion around the vessel axis depending on the axial stretch ratio. A Riemannian stress-free configuration of artery is adopted to analyze stress distributions. It is determined from experimentally investigated deformations of arterial ring radially cut and axial strip sectioned. The stress-free configuration is considered as a Riemannian manifold that is not Euclidean. A strain energy function is adopted to analyze stresses. Torque is linearly related to torsion of vessel axis under a physiological condition. The shear component of deformation gradient almost linearly increases from the inner surface of vessel to the outer surface with discontinuity at the boundary between media and adventitia. The shear stress also increases from the inner surface to the outer surface. The shear stress is greatly larger in the adventitia than in the media-intima.</p>