Abstract: A mass flow meter for flowing media, which operates according to the Coriolis principle, has a straight Coriolis measuring tube, an oscillation generator acting on the Coriolis measuring tube, and at least one sensor detecting Coriolis forces and/or Coriolis oscillations based on Coriolis forces. The problem which results from the fact the mass flow meter has only one straight Coriolis measuring tube is largely eliminated by designing the Coriolis measuring tube as a flow channel of a thick-walled body, namely a thick-walled tube, the thick-walled tube having recesses accessible from the outside and reaching very close to the Coriolis measuring tube. A vibration transducer as the oscillation generator acts upon the residual material of the thick-walled tube remaining in the area of the recesses, and the Coriolis forces or Coriolis oscillations appearing in the area of the residual material of the thick-walled tube are detected by each sensor.