The disclosure relates to a Coriolis mass flowmeter with an oscillatable straight measuring tube consisting of a corrosion-resistant metal, in particular of titanium or a titanium alloy, to which are attached mounted parts connected directly to the measuring tube for the implementation of the Coriolis measurement principle. Furthermore, stabilizing elements running parallel to the measuring tube are coupled to the measuring tube via mounted parts connected directly to the measuring tube, the mounted parts and the stabilizing elements consisting of a metal other than that of the measuring tube. The stabilizing elements are manufactured from a second material which possesses a coefficient of thermal expansion adapted to the metal of the measuring tube. The mounted parts connected directly to the measuring tube are manufactured from a third material which possesses a higher coefficient of thermal expansion than the metal of the measuring tube.