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. Since

the metamaterials used to implement cloaking are based on effective

medium theory, the resulting large variation in D and B will pose a

challenge to the suitability of the field averaged characterization of "

and 碌. We also consider cloaking with and without the SHS (softand-

hard surface) lining, shown in [6] to be theoretically necessary

for cloaking in the cylindrical geometry. 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.