A quartz crystal microbalance (QCM) is described, which is based on a torsional resonator, rather than a conventional thickness-shear resonator. Typical applications are measurements of film thickness in the coating industry and monitoring of biofouling. The torsional QCM is about a factor of 100 less sensitive than the conventional QCM. On the other hand, it can probe film thicknesses in the range of hundreds of microns, which is impossible with the conventional QCM due to viscoelastic artifacts. Data acquisition and data analysis proceed in analogy to the conventional QCM. An indicator of the material's softness can be extracted from the bandwidth of the resonance. Within the small-load approximation, the frequency shift is independent of whether the sample is applied to the face or to the side of the cylinder. Details of the geometry matter if the viscoelastic properties of the sample are of interest.