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Cloaking of static magnetic fields by a finite thickness type-IIsuperconductor tube being in the full critical state and surrounded by acoaxial paramagnet shell is studied. On the basis of exact solutions to theMaxwell equations, it is shown that, additionally to previous studies assumingthe Meissner state of the superconductor constituent, perfect cloaking is stillrealizable at fields higher than the field of full flux penetration into thesuperconductor and for arbitrary geometrical parameters of both constituents.It is also proven that simultaneously the structure is fully undetectable underthe cloaking conditions. Differently from the case of the Meissner state thecloaking properties in the application relevant critical state are realized,however, only at a certain field magnitude.

Magnetic cloaking by a paramagnet/superconductor cylindrical tube in the critical state