This mass flow/density sensor (10), which can be installed in a pipe and through which a fluid to be measured flows during operation, is to be balanced over a wide density range, so that accurate measurements are possible. A single straight measuring tube (13) having a longitudinal axis (131) extends between its inlet end (11) and the outlet end (12) and is fixed to a support, e.g., a cylindrical tube (14, 14'). The support has a longitudinal centroidal line (141) which is parallel to, but does not coincide with, the longitudinal axis (131) of the measuring tube. A cantilever (15) is fixed to the measuring tube (13) midway between the inlet and outlet ends (11, 12) and in operation causes the measuring tube to vibrate either in a first fundamental flexural mode or in a second fundamental flexural mode having a higher frequency than this first mode. An excitation arrangement (16) disposed midway between the end pieces excites the measuring tube (13) in the second mode. Sensors (17, 18) for the motions of the measuring tube on the inlet and outlet side are positioned between the middle of the tube and the inlet and outlet ends, respectively. The support may be provided with a counterbalance. Because of the torsional vibrations exerted by the cantilever on the measuring tube, the sensor is also well suited for measuring the viscosity of the fluid.