A new method of noninvasive examinations of the forward and reflected (backward‐traveling) pressure waves in human arteries is presented. The study concerned the effect of an artery stenosis on the value of the reflection coefficient modulus and the time delay of the reflected wave relative to the forward wave. The investigations were carried out in the common carotid artery of a healthy person and of a person with 60% stenosis of the internal carotid artery. The instantaneous value of the blood pressure in the common carotid artery was determined from ultrasonic measurement of the instantaneous artery diameter and from the systolic and diastolic blood pressures measured by cuff in the brachial artery. The coefficient of wave reflection was calculated on the basis of noninvasive ultrasonic investigations of the characteristic and input impedance in the common carotid artery. The results of the examinations indicate that a vessel stenosis causes an increase in the value of the reflection coefficient modulus and a decrease in the time delay between the reflected and forward pressure waves at the measurement point just proximal the stenosis. This observation can be of significance for noninvasive diagnosing of atherosclerosis of arterial vessels.