A solid cylinder set into torsional oscillation at its natural frequency has been used to measure the viscosity of liquid helium in the range 4.2 ° K. to 1.2 ° K. Values of the viscosity calculated from the logarithmic decrement of the decay of the oscillations at the natural frequency of 11.8 kc./sec. of the cylinder are in good agreement within the errors, which are of the order of 30%, with the most recent oscillating disk values. Values obtained at a frequency of 35.5 kc./sec. (a harmonic of the cylinder) might be of the order of 10% lower. The depth of penetration of the viscous waves in these experiments was less than 5 × 10−5 cm.