A device for measuring the mass rate of flow according to the Coriolis principle, with two measurement tubes at least in one section of which runs in a common plane, and a connector by which the two measurement tubes are connected to one another where they run in a common plane. The connector has a stiffening plate which is parallel to the common plane of the measurement tubes and which is attached to the two measurement tubes. At least one stiffening fin is provided on the stiffening plate so that the bending stiffness of the connector for bending in the common plane of the measurement tubes in which, generally, excitation vibrations of the measurement tubes also take place, is made greater than the torsional stiffness of the connector for torsional vibrations. As a result, the measurement accuracy of the Coriolis mass flow rate measurement device is improved.