A Coriolis mass flowmeter having at least four measuring tubes running parallel, the measuring tubes being joined in pairs into a oscillation unit by being inserted in openings in a holding device (1) and wherein at least part of either a sensor or actuator device is attached to the holding device (1). A Coriolis mass flowmeter that has an increased measuring accuracy is implemented in that the measuring tube central axes (3) of a measuring tube pair span a common plane (E), that the holding device (1) has at least two attachment extensions (4), that the attachment extensions (4) extend across the common plane (E) and that the holding devices (1) with the attachment extensions (4) are mirror symmetric relative to the common plane (E) in respect to their projection viewed in the direction of the measuring tube central axes (3).