The forced harmonic torsional oscillation of an inertialess finite rigid cylinder clamped in a circular borehole in an elastic half space is investigated. The displacement field is axisymmetric, involving only angular motions. The problem is formulated in terms of a Fredholm integral equation of the first kind. An approximate solution for the shear stress distribution acting at the interface of the oscillator and the borehole wall is obtained using the Bubnov-Galerkin method. Numerical results for the resultant torque required to provide a unit rotation of the oscillator are presented. These results may be useful for prediction of soil shear wave speeds.