Stroke and myocardial infarction are initiated by rupturing vulnerable atherosclerotic plaques. With noninvasive ultrasound elastography, these plaques might be detected in carotid arteries. However, since the ultrasound beam is generally not aligned with the radial direction in which the artery pulsates, radial and circumferential strains need to be derived from axial and lateral data. Conventional techniques to perform this conversion have the disadvantage that lateral strain is required. Since the lateral strain has relatively poor accuracy, the quality of the radial and circumferential strains is reduced. In this study, the radial and circumferential strain estimates are improved by combining axial strain data acquired at multiple insonification angles. Adaptive techniques to correct for grating lobe interference and other artifacts that occur when performing beam steering at large angles are introduced. Acquisitions at multiple angles are performed with a beam steered linear array. For each beam steered angle, there are two spatially restricted regions of the circular vessel cross section where the axial strain is closely aligned with the radial strain and two spatially restricted regions (different from the radial strain regions) where the axial strain is closely aligned with the circumferential strain. These segments with high quality strain estimates are compounded to form radial or circumferential strain images. Compound radial and circumferential strain images were constructed for a homogeneous vessel phantom with a concentric lumen subjected to different intraluminal pressures. Comparison of the elastographic signal-to-noise ratio (SNR(e)) and contrast-to-noise ratio (CNR(e)) revealed that compounding increases the image quality considerably compared to images from 0 degrees information only. SNR(e) and CNR(e) increase up to 2.7 and 6.6 dB, respectively. The highest image quality was achieved by projecting axial data, completed with a small segment determined by either principal component analysis or by application of a rotation matrix.