  The transformation theory of optics and acoustics is developed for the
equations of linear anisotropic elasticity. The transformed equations
correspond to non-unique material properties that can be varied for a given
transformation by selection of the matrix relating displacements in the two
descriptions. This gauge matrix can be chosen to make the transformed density
isotropic for any transformation although the stress in the transformed
material is not generally symmetric. Symmetric stress is obtained only if the
gauge matrix is identical to the transformation matrix, in agreement with
Milton et al. (2006). The elastic transformation theory is applied to the case
of cylindrical anisotropy. The equations of motion for the transformed material
with isotropic density are expressed in Stroh format, suitable for modeling
cylindrical elastic cloaking. It is shown that there is a preferred approximate
material with symmetric stress that could be a useful candidate for making
cylindrical elastic cloaking devices.
