Display omitted •1st a new device for the measurement of damped torsional oscillation is experimentally characterized and theoretically modeled.•2nd a device for the measure of viscosity in liquids is fabricated and applied to monitor milk viscosity as function of fat content and temperature.•3rd the main novelty consists in the fact that the measurement is performed by detecting the logarithmic decrement of oscillation as damped by the viscous forces.•4th the magnetoelastic sensor operates outside the liquid to be monitored thus avoiding any contamination or inferences.•5th the proposed device enables to have good viscosity determination at low share rate, in the range where standard rheometer fail. A new application of a high sensitivity magnetoelastic resonator able to measure period and damping constant of low frequency torsional oscillation is described and validated by experimental tests. The sensitive parameter is the amplitude of resonant magnetoelastic waves in the soft ferromagnetic core (Fe62.5Co6Ni7.5Zr6Cu1Nb2B15 amorphous ribbon). The theoretical model of the device has been developed, correlating torsional oscillations to the friction force applied by the fluid in which they occur. Thus, an accurate indirect evaluation of fluid viscosity has been demonstrated. The main prerogative of the proposed sensor is to work without contact with the oscillating mechanism. As experimental validation, viscosity of UHT milk was measured versus different fat content. The experimental comparison with a standard rheometer demonstrates the new device competitiveness in the measure of low viscosity fluids at low share rate. Moreover, the detected behaviors at increasing temperature are in agreement with previous literature. In perspective, the new magnetoelastic resonators application can be very ductile and effective in on-line monitoring of viscosity change with time to control composition, degradation or contamination of liquids.