This paper proposes a method for qualitatively estimating the mechanical properties of arterial walls on a beat-to-beat basis through noninvasive measurement of continuous arterial pressure and arterial diameter using an ultrasonic device. First, in order to describe the nonlinear relationships linking arterial pressure waveforms and arterial diameter waveforms as well as the viscoelastic characteristics of arteries, we developed a second-order nonlinear model (called the log-linearized arterial viscoelastic model) to allow estimation of arterial wall viscoelasticity. Next, to verify the validity of the proposed method, the viscoelastic indices of the carotid artery were estimated. The results showed that the proposed model can be used to accurately approximate the mechanical properties of arterial walls. It was therefore deemed suitable for qualitative evaluation of arterial viscoelastic properties based on noninvasive measurement of arterial pressure and arterial diameter.