The transducer (1) has at least one at least temporarily vibrating flow tube (101) of predeterminable lumen for conducting a fluid. The flow tube (101) communicates with a connected pipe via an inlet tube section (103), ending in an inlet end, and an outlet tube section (104), ending in an outlet end, and in operation performs flexural vibrations about an axis of vibration joining the inlet and outlet ends. The flow tube (101) has at least one arcuate tube section (101c) of predeterminable three-dimensional shape which adjoins a straight tube segment (101a) on the inlet side and a straight tube segment (101b) on the outlet side. At least one stiffening element (111, 112) is fixed directly on or in close proximity to the arcuate tube segment (101c) to stabilize the three-dimensional shape. By means of the at least one stiffening element (111, 112), the cross sensitivity of the transducer (1) is greatly reduced, so that cross talks from pressure to mass flow signals are minimized and the accuracy of the transducer is improved.