Arterial elasticity has become a topic of importance in the past decades, as it has shown that it can be used to predict cardiovascular diseases and mortality. Several in vivo and ex vivo techniques have been developed to characterize the mechanical properties of vessels. In vivo techniques tend to ignore the anisotropicity of the vessel wall components. While ex vivo techniques tend to be destructive and do not to account for the geometry of the arteries. In this paper we present a technique using sonometry to study the elasticity of soft tubes and excised pig carotids in different directions. The method uses piezoelectric crystals to track the strain in the circumferential and longitudinal directions while the tubes or vessels are being pressurized. We compare the Young's moduli obtained from sonometry experiments performed in two different types of tubes with the mechanical testing done in the material used to make these tubes. We also present data obtained in the excised pig carotids and show the differences in the longitudinal versus the circumferential directions. The technique we propose has a potential for the non destructive study of soft material cylindrical shapes and can be use to study the mechanical properties of vessels.