  We analyse the elastic properties of a class of cylindrical cloaks deduced
from linear geometric transforms ${\bf x} \to {\bf x}'$ in the framework of the
Milton-Briane- Willis cloaking theory [New Journal of Physics 8, 248, 2006].
More precisely, we assume that the mapping between displacement fields ${\bf
u}({\bf x}) \to {\bf u}'({\bf x}')$ is such that ${\bf u}'({\bf x}') = {\bf
A}^{-t}{\bf u}({\bf x})$, where ${\bf A}$ is either the transformation gradient
$F_{ij} = \partial x'_i/ \partial x_j$ or the second order identity tensor
${\bf I}$. The nature of the cloaks under review can be three-fold: some of
them are neutral for a source located a couple of wavelengths away; other lead
to either a mirage effect or a field confinement when the source is located
inside the concealment region or within their coated region (some act as
elastic concentrators squeezing the wavelength of a pressure or shear polarized
incident plane wave in their core); a last category of cloaks is classified as
an elastic counterpart of electromagnetic perfect cylindrical lenses. The
former two categories require either rank-4 elastic tensor and rank-2 density
tensor and additional rank-3 and 2 positive definite tensors $({\bf A} = {\bf
F})$ or a rank 4 elasticity tensor and a scalar density $({\bf A} = {\bf I})$
with spatially varying positive values. However, the latter example further
requires that all rank-4, 3 and 2 tensors be negative definite $({\bf A} = {\bf
F})$ or that the elasticity tensor be negative definite (and non fully
symmetric) as well as a negative scalar density $({\bf A} = {\bf I})$. We
provide some illustrative numerical examples with the Finite Element package
Comsol Multiphysics when ${\bf A}$ is the identity.
