Abstract: The presence of a longitudinal constraint must be conceived physiologically as due largely to the connective tissue attachments on the outside of the artery. Living tissues are yisco-elastic bodies. In order to analyse the effect of external visco-elastic tissue to pulsatile flow in arteries, in this paper the external connective tissue of artery will be considered as a Voigt visco-elastic body, and the expressions of pulse wave velocity and the velocity of pulsatile flow will be found by the velocity of pulsatile flow will be found by the blood motion equations (Navier-Stokes equation) as well as wall motion equations (Lamb equation). The results of free elastic tube^[4] and those of external elastic restraint^[6] by Womersley can be considered as a particular case and can be covered in this paper.

Key words: second-order nonholonomic system, Lie symmetry, conserved quantity