Mass flow sensor according to the Coriolis principle, comprising: at least a measuring tube which can vibrate designed to conduct a medium whose flow is to be measured; at least one exciter designed to excite vibrations of the measuring tube; at least two sensors designed to measure the vibrations of the measuring tube and to output first and second sensor signals that depend on the vibration oscillations; and at least an operation and evaluation unit to drive the exciter, to capture the sensor signals and to determine a mass flow measured value on the basis of a phase difference or a time difference between the sensor signals, said value being, in a first approximation, proportional to the mass flow; wherein the vibration behavior of the measuring tube has a cross-sensitivity to the viscosity of the medium, characterized in that the cross-sensitivity correlates to a Stokes number for Reynolds numbers at least below a lower Reynolds number limit value, in that the phase difference or the time difference of the sensor signals has a cross-sensitivity correlating to the Stokes number, in that the operation and evaluation unit is designed, at least for Reynolds numbers below the lower Reynolds number limit value, to determine a current value of the Stokes number depending on a diameter of the measuring tube, a characteristic vibration frequency of the measuring tube and a viscosity of the medium flowing through the measuring tube, wherein the Stokes number is an indicator of the depth of penetration of the vibration oscillations of the measuring tube in the medium, and in that the operation and evaluation unit is designed to compensate for the influence of the cross-sensitivity depending on the current value of the Stokes number when determining the mass flow. at least a measuring tube which can vibrate designed to conduct a medium whose flow is to be measured; at least one exciter designed to excite vibrations of the measuring tube; at least two sensors designed to measure the vibrations of the measuring tube and to output first and second sensor signals that depend on the vibration oscillations; and at least an operation and evaluation unit to drive the exciter, to capture the sensor signals and to determine a mass flow measured value on the basis of a phase difference or a time difference between the sensor signals, said value being, in a first approximation, proportional to the mass flow; wherein the vibration behavior of the measuring tube has a cross-sensitivity to the viscosity of the medium, characterized in that the cross-sensitivity correlates to a Stokes number for Reynolds numbers at least below a lower Reynolds number limit value, in that the phase difference or the time difference of the sensor signals has a cross-sensitivity correlating to the Stokes number, in that the operation and evaluation unit is designed, at least for Reynolds numbers below the lower Reynolds number limit value, to determine a current value of the Stokes number depending on a diameter of the measuring tube, a characteristic vibration frequency of the measuring tube and a viscosity of the medium flowing through the measuring tube, wherein the Stokes number is an indicator of the depth of penetration of the vibration oscillations of the measuring tube in the medium, and in that the operation and evaluation unit is designed to compensate for the influence of the cross-sensitivity depending on the current value of the Stokes number when determining the mass flow. <EOS>