Three dimensional (3D) modelling of arteries using noninvasive ultrasound aims to improve visualisation of the artery under consideration and in particular the detection of disease within it. Such a technique needs to handle the speckle contaminating ultrasound images. A set of arterial wall templates are used for reconstruction which are determined by feature extraction from the ultrasound images. The arterial wall data is determined after a circular approximation to the artery has been identified. This circle is extracted from the edge magnitude information. The circle is located using an implementation of the Hough transform tailored to determine the contour which best fits the arterial data. The deviation from this circle provides the arterial wall template except when data is absent when the approximation itself is used. By extracting the template from successive ultrasound images in in vivo studies, 3D pictures of vessels have been developed. These are portrayed using oblique projection and work is in progress to improve the 3D visualisation and to establish the accuracy of this new approach using a test object.