Similar to the resonant‐sphere method in its experimental aspect, a resonant‐cylinder technique is developed for the measurement of the internal friction of solids. The solutions of the theoretical problems of using the cylinder instead of sphere are presented: the computation of the resonance spectrum of the cylinder (axially symmetric modes only); the evaluation of theQfactor from the experimental resonance spectrum, characterized by a low (peak/background) ratio; and the separation of the dilatational and shear oscillation components in the total value of internal friction, measured for a given resonance mode. The anisotropy of viscoelastic parameters in a rolled bar of commercial steel has been measured as a method sensitivity check. Other preliminary experimental data are also presented as illustrative examples.