We analyze 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 material parameters tend towards the singular ideal cloaking values, 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 poses a challenge to the suitability of the field-averaged characterization of epsilon and mu. 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.