  We analyze, both analytically and numerically, the effectiveness of cloaking
an infinite cylinder from observations by electromagnetic waves in three
dimensions. We show that, as truncated approximations of the ideal permittivity
and permeability tensors tend towards the singular ideal cloaking fields, so
that the anisotropy ratio tends to infinity, the $D$ and $B$ fields blow up
near the cloaking surface. We also consider cloaking with and without the SHS
(soft-and-hard surface) lining. We demonstrate numerically that cloaking is
significantly improved by the SHS lining, with both the far field of the
scattered wave significantly reduced and the blow up of $D$ and $B$ prevented.
