Objective. Measuring waves induced with acoustic radiation force (ARF) in arteries has been studied over the last decade. To date, it remains a challenge to quantitatively assess the local arterial biomechanical properties. The cylindrical shape and waveguide behavior of waves propagating in the arterial wall pose complexities to determining the mechanical properties of the artery. Approach. In this paper, an artery-mimicking tube in water is examined utilizing three-dimensional measurements. The cross-section of the tube is measured while a transducer is translated over 41 different positions along the length of the tube. Motion in the radial direction is calculated using two components of motion which are measured from the two orthogonal views of the cross-section. This enables more accurate estimation of motion along the circumference of tube. Main results. The results provide more information to categorize the motion in tube wall into two types of responses: a transient response and a steady state response. The transient response is caused by ARF application and the waves travel along the length of the tube for a relatively short period of time. This corresponds to the axial and circumferential propagating waves. The two circumferential waves travel along the circumference of tube in CW (clockwise) and CCW (counter-clockwise) direction and result in a standing wave. By using a directional filter, the two waves were successfully separated, and their propagation was more clearly visualized. As a steady state response, a circumferential mode is generated showing a symmetric motion (i.e., the proximal and distal walls move in the opposite direction) following the transient response. Significance. This study provides a more comprehensive understanding of the waves produced in an artery-mimicking tube with ARF application, which will provide opportunities for improving measurement of arterial mechanical properties.