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The constant increase in mass of the cryostats, containment tanks, passive shielding and other mechanical elements of the modern low background detectors put more stringent requirements on their radiopurity levels. In general they has to be ~1 mBq/kg of U238 / Th232 or lower, which means that mass concentration should be < 0.1 ppb for U and < 0.25 ppb for Th. Traditionally, the field relies on specially selected low background stainless steel, electrochemical oxygen-free copper, or a combination of the two. However, the most promising material in terms of physical and mechanical properties is titanium (or its alloys). Our study of various Ti samples show that the levels of contaminations of commercially available industrial titanium can varies from 0.2 to 400 mBq/kg for U/Th. Therefore, the only possible way to obtain the material with a low and controlled level of contamination is to develop (or improve the existing) the production technology and to build the dedicated manufactory line.