Fine tube stents are used for maintaining localised flow in stenotic blood vessels. Elasticity and plasticity for expansion, rigidity for resisting bending under force and strength to prevent unexpected failure, are required properties of the tubes from which these stents are formed. Biomedical metastable β titanium alloys have been developed as implant materials for a large number of biomedical applications due to a combination of favourable characteristics, e.g. good biocompatibility, excellent toughness and corrosion resistance. A metastable β alloy, Ti-25Nb-3Mo-3Zr-2Sn, has been developed without toxic alloying elements, which is a promising candidate material for stent applications. Metallic materials used for stents are commonly not biodegradable and implanted in the vessel permanently, which may provoke in-stent restenosis and stent thrombosis. In order to remove the implanted materials after service, biodegradable materials, absorbed by the body slowly, are also a field of research interest. Magnesium alloys have been used in studies for biomedical stent applications as a new biodegradable material. Magnesium stents can reopen the blocked blood vessels temporarily before degrading in physiological environments. In addition to the biodegradable characteristics, their mechanical properties are reasonable. The Mg-3Al-1Zn (AZ31) alloy is the subject of some research on the processing of biomedical magnesium alloys as it is a commonly available commercial alloy. Consequently, the Ti-25Nb-3Mo-3Zr-2Sn alloy and the AZ31 magnesium alloy have been used in this thesis to investigate the evolution of mechanical properties and microstructure in the processing of fine tubes.The deformation mechanisms during cold deformation of metastable β titanium alloys are mainly associated with martensitic phase transformations and mechanical twinning. It has been reported that stress-induced phase transformations and {112}〈111〉, {332}〈113〉 twinning modes may be activated under different stress states in metastable β titanium alloys. They can exhibit varying elasticity, Young's modulus and strain hardening behaviour. Because the martensitic start temperature is below room temperature for most metastable β titanium alloys, the α″ martensitic transformation can easily occur under a small amount of external stress. Mechanical twins were reported to hinder slip and dislocation motion thereby increasing the strain hardening rate. The development of β and α″ texture during processing is another critical influence on the mechanical properties of fine tubes. Therefore, studies on the martensitic transformation, mechanical twins and texture evolution is of significance in order to understand the processing of β titanium fine tubes.ii Magnesium alloys deform through the formation of a large amount of mechanical twins due to the relatively low critical stress to activate twinning in comparison with 〈 + 〉 slip. There are typically two primary mechanical twinning modes for magnesium alloys, {101 ̅ 2} extension twins and {101 ̅ 1} cont...