Increased stiffness of the 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. From measured PWV, the diameter and thickness of the artery are needed to calculate the elastic modulus of the artery. In this paper a new method of using ring resonant mode for estimation of arterial elastic modulus is proposed. To generate the ring resonance, a localized radiation force of ultrasound is remotely and non-invasively applied at the artery. The vibration response of the artery is measured by optical or Doppler techniques. Three ring resonant modes are identified for estimation of the elastic modulus of the artery. Experiments on ring resonant frequencies were carried out on a porcine artery. The measurement results of the three resonant frequencies are, respectively, 356 Hz, 718 Hz, and 968 Hz. Estimation of the circumferential Young's modulus by the three measured frequencies are, respectively, 135 kPa, 137 kPa, and 125 kPa. The estimated modulus is very consistent with the three resonant frequency measurements. The values of these three estimations are well within the range of arterial elastic modulus from published papers. With this method, the estimation of the Young's modulus of the artery only requires the diameter of the artery, but doesn't need the thickness of the artery which is difficult to measure with accuracy and precision.