GeTe is a material of intense topical interest due to its potential in the context of phase-change and nanowire memory devices, as a base for thermoelectric materials and as a ferroelectric. The combination of a soft optic mode and a Peierls distortion contributes large strains at the cubic – rhombohedral phase transition near 625 K and the role of these has been investigated through their influence on elastic and anelastic properties by resonant ultrasound spectroscopy. The underlying physics is revealed by softening of the elastic constants by ~30-45%, due to strong coupling of shear and volume strains with the driving order parameter and consistent with an improper ferroelastic transition which is weakly first order. The magnitude of the softening is permissive of the transition mechanism involving a significant order/disorder component. A Debye loss peak in the vicinity of 180 K is attributed to freezing of the motion of ferroelastic twin walls and the activation energy of ~0.07 eV is attributed to control by switching of the configuration of long and short Ge-Te bonds in the first coordination sphere around Ge. Precursor softening as the transition is approached from above can be described with a Vogel-Fulcher expression with a similar activation energy, which is attributed to coupling of acoustic modes with an unseen central mode that arises from dynamical clusters with local ordering of the Peierls distortion. The strain relaxation and ferroelastic behaviour of GeTe depend on both displacive and order/disorder effects but the dynamics of switching will be determined by changes in the configuration of distorted GeTe₆ octahedra, with a rather small activation energy barrier.