The arterial elasticity was evaluated by ultrasonic measurements of the logarithmic coefficient of the artery wall stiffness α and by the local pulse wave velocity. The measurements were carried out on the model of the artery constructed as the elastic silicone pipe immersed in the water tank. Two synchronized ultrasonic apparatus, called Vascular Echo Doppler (VED), developed by the author, were used for ultrasonic radio frequency (RF) echoes acquisition. The pulse wave was determined by the non-invasive ultrasonic measurement of the internal vessel diameter on the basis on the zero-crossing method. The pulse wave velocity was determined by the transit time measurement of the pulse wave between two measurement points located 5cm along the section of the model of the artery. The transit time measurement was based on the criteria of similarity of the first derivatives of the raising slopes of the pulse waves simultaneously recorded. The pulse wave velocity based of the transit time measurement was referred to the pulse wave velocity calculated on the basis of the well-known modified Bramwell-Hill relation as well as to the logarithmic coefficient of the artery wall stiffness α.