Pulse wave velocity often used as an indicator clinically for diagnosis of cardiovascular diseases. This assumption is well grounded in the physics of pulsatile flow of an incompressible fluid where it is fully established that a pulse wave travels faster in a tube of stiffer wall, the wave speed becoming infinite in the mathematical limit of a rigid wall. in this paper we point out that pulse wave velocity in a stiffer tube is strictly valid only when the wall is free from outside constraints, Which is used as the outer boundary condition (tethering: the degree to which the vessel wall is surrounded by tissue). In this paper, using the equations of blood fluid and vessel walls and using analytical solutions and the use of tethering as outer boundary conditions pulse wave velocity is investigated. In previous research pulse wave velocity has been obtained just for the tethering zero and one, But in the study pulse wave velocity investigated for tethering different degrees of tethering and for three different material wall viscoelastic, elastic and stiff. With this research, it is clear the changes of pulse wave velocity with change of degrees of tethering and change of material wall ,This results is a great help for use of pulse wave velocity as an clinical index to predict arterial stiffness.