This paper proposes a novel technique to support the monitoring of peripheral vascular conditions using biological signals such as electrocardiograms, arterial pressure values and pulse oximetry plethysmographic waveforms. In this approach, a second-order log-linearized model (referred to here as a log-linearized peripheral arterial viscoelastic model) is used to describe the non-linear viscoelastic relationship between blood pressure waveforms and photo-plethysmographic waveforms. The proposed index enables estimation of peripheral arterial wall stiffness changes induced by sympathetic nerve activity. The validity of the method is discussed here based on the results of peripheral vascular condition monitoring conducted during endoscopic thoracic sympathectomy (ETS). The results of ETS monitoring showed significant changes in stiffness variations between the periods before and during the procedures observed (p < 0.01) as well as during and after them (p < 0.01), so that it was confirmed that sympathetic nerve activity is drastically decreased in the area around the monitoring site after the thoracic sympathetic nerve trunk on the monitoring side is successfully blocked. In addition, no change was observed in the values of the proposed index during the ETS procedure on the side opposite that of the monitoring site. The experimental results obtained clearly show the proposed method can be used to assess changes in sympathetic nerve activity during ETS.