Abstract: An improved technique for establishing the position, dimensions and orientation of a vessel which is essentially free of internal acoustic discontinuities involves scanning the vessel with a beam of ultrasonic energy and, from the ultrasonic echoes received in the A-mode lines of sight of the ultrasonic beam, establishing a B-mode image of the vessel. An angle marker, in the form of a short line segment, is established, using the B-mode image, on or near a straight axis of the vessel. The length of the angle marker is divided into a number of sub-sectors, each of which receives approximately the same number of A-mode lines of sight of the ultrasonic beam. An average A-mode signal is obtained for each sub-sector. Comparison of the average A-mode signals provides information about the orientation of the angle marker relative to the axis of the vessel.