A measurement of G which will use a torsion pendulum in the `dynamic' (time-of-swing) mode, measuring the influence of field source masses on the pendulum's oscillation period, is being prepared at UC Irvine. Features of the design include: (i) operation at cryogenic temperature (2 K) to reduce thermal noise and increase frequency stability and for ease of magnetic shielding, (ii) large pendulum oscillation amplitudes to increase signal-to-noise ratio and reduce the effect of amplitude-determination error, (iii) use of a pair of source mass rings to produce an extremely uniform field gradient; and (iv) use of a thin quartz plate as a torsion pendulum to minimize sensitivity to pendulum density inhomogeneity and dimensional uncertainties. The `dynamic' method to be used has the great advantage of requiring no angular displacement measurement or calibrating force, but, as pointed out by Kuroda, the method is subject to systematic error associated with the anelastic properties of a torsion fibre. We demonstrate that, for the linear anelasticity discussed by Kuroda, the fractional error introduced by anelasticity in such measurements of G is bounded by 0 G/G½Q^-1, where Q is the torsional oscillation quality factor of the pendulum. We report detailed studies of anelasticity in candidate fibre materials at low temperature, concluding that anelastic behaviour should not limit our G measurement at a level of a few ppm.