Why can x-rays pass and not radio waves? If we stand in an elevator or other metal containers we lose radio signals etc the very same reason for which we cannot see across a block of metal that light cannot penetrate it. However x-rays and gamma rays can.
Now if you see the working of Faraday's cages then from weak to very strong no electric field passes through them which is why they are safe!
Now I would draw the simple conclusion that atleast one part of EM radiation must not be penetrating any metal surface and since EM radiations cannot survive solely as E or M radiation any sort of radiation penetrating metal surface must not be possible. 
But in fact x-rays do pass metal surfaces.  How can this happen when clearly atleast electric field part of radiation must not penetrate the block?
 A: A Faraday cage need not be a continuous conductor — you can make a reasonable Faraday cage out of chicken wire. The rule of thumb is that if the gaps in the conductor are small compared to the wavelength of the electromagnetic wave, the wave "won't notice" and the conductor will appear continuous; if the gaps are bigger than the wavelength, parts of the signal can pass through the cage without interaction.  So a chicken-wire Faraday cage could be a good blocker of meter-scale radio waves, but would definitely be a poor blocker of millimeter-wave radio.
X-rays and gamma rays have wavelengths comparable to or smaller than the spacing between atoms in a metal, so even a solid piece of metal "looks like" a chicken-wire fence with lots of gaps.
An alternative explanation (which isn't as different as it might seem) is that radio waves can transfer energy to many of conduction electrons at once, making them slosh around.  But there aren't any high-frequency collective motions for bound electrons in the conductor, so x-rays and gamma rays tend to excite single electrons and to give them enough energy that they essentially become free particles. (This is "Compton scattering"; photons above 1 MeV can also lose energy by creating electron-positron pairs.) Since the electron motion isn't collective, it doesn't really matter any more whether the electrons were conducting or not beforehand, and so conductors don't really make better shields for x-rays and gamma rays than similarly-dense insulators.
A: The E-field cancelling effect of Faraday cages is a macroscopic effect; an external electric field induces forces on charge carriers in the cage such that the charge carriers rearrange themselves so that the E-field within the cage is zero.  
However, when the electric field is oscillating, as in a EM radiation, these charge carriers are constantly moving in their quest to oppose the change in E-field within the cage.  When the frequency is high enough, the charge carriers of a given mesh size (for perforated shielding) cannot effectively resist penetration.  The size of the holes in perforated shielding must be smaller than the wavelength of the radiation.
Once you have a solid sheet of metal as a shield, microscopically, you essentially have a very small mesh (on the order of crystal lattice spacing). There is a threshold frequency $f_0$ here as well such that for radiation with frequency $f>f_0$ (i.e., $\lambda <$ lattice spacing), the radiation can penetrate the shielding.  The frequency of x-ray ($f>10^{18}Hz$, $\lambda < 10^{-10}m$) and gamma rays ($f>10^{20}Hz$, $\lambda < 10^{-12}m$) are sufficiently high that common metal shielding is often insufficient to completely shield.
A: @Bill mentioned the threshold frequency - it's actually the plasma frequency (http://en.wikipedia.org/wiki/Plasma_oscillation ), up to a coefficient. The plasma frequency of free electrons in metal is significantly lower than the frequency of gamma-rays, so the plasma cannot shield gamma-rays.
A: The effectiveness of a Faraday cage depends on the conductivity at the frequency of interest.
At very high frequencies the inertia of the electrons becomes a significant factor: the E field just can't "jiggle" the electrons very much as they are "relatively massive". This means there will be little induced current and little attenuation of the EM wave. By contrast at lower frequencies the mass of the electrons is relatively less important and thus the movement of the electrons in twosomes to the EM wave is better.
Looking at the X ray as a particle, it is very small and doesn't "see" most of the electrons in the metal - so again the probability of an interaction is quite small and most of the X-rays will pass through a thin sheet of metal unperturbed.
