Increased stiffness of arteries has recently gained acceptance as an independent risk factor for cardiovascular and many other diseases. Pulse wave velocity (PWV) is widely used for estimating the stiffness of an artery. However, PWV is an average indicator of artery stiffness between the two measuring points, and therefore does not identify local stiffness. In addition, the thickness of artery is needed to calculate artery elastic modulus. We have discovered that there are certain ring resonance modes of arteries that can be used for measuring local arterial elastic modulus. These modes can be excited by remote "palpation" with selectively placed ultrasonic radiation force. The resulting vibration of artery is measured with optical or Doppler ultrasound methods. Experiments on ring resonance were carried out on femoral arteries of pig in vitro and in vivo. This family of resonances occurs at relatively low frequency, around 375 Hz for the artery in vivo. Estimation of Young's modulus of artery is 112 kPa by the ring frequency 375 Hz without the requirement of the arterial thickness.