Gravitational shielding and equivalence principle I read on wiki that gravitational shielding is considered to be a violation of the equivalence principle. Is that so, How? A conceptual description without lot of mathematics will be helpful. 
I am not sure whether the wiki article refers to shielding only by materials, or it also includes mechanisms - e.g a rotating disk. I know rotating disk does not shield gravity, but just to describe what a mechanism could mean.
It goes on to say that any evidence of gravitational shielding would falsify GR, is this true?
It is hard for me to believe because - suppose gravitational shielding is demonstrated somehow, then how GR can be falsified all of a sudden, which has been verified by so many experiments and phenomena. So, that makes me think gravitational shielding would not invalidate GR.
 A: The shielded body would have to have an inertial mass that is different than its gravitational mass, since it is gravitational mass that would get reduced in shielding. The gravitational mass causes weight, the inertial mass resistance to acceleration. The equivalence principle says they are the same (equivalent). Plenty of experiments showing they are, and that shielding doesn't work. 
See the wiki article for the equivalence principle at  https://en.m.wikipedia.org/wiki/Equivalence_principle. In the wiki article on shielding gravity it describes the measurements and experiments -- see it at https://en.m.wikipedia.org/wiki/Gravitational_shielding. 
Yes, that wiki article should be edited to not make it mysterious why shielding invalidates the Equivalence principle, as written it says 'it is considered', not a very scientific statement.  
A: The Wikipedia article refers to the paper General Theory of Relativity: Will it survive the next decade? by Orfeu Bertolami, Jorge Paramos and Slava G. Turyshev. In that paper gravitational shielding is discussed in section 3.4 on pages 16–17.
Rather than consider specific mechanisms the article discusses the general possibility that matter itself screens gravity, so for example Newton's law for the force between two bodies would be modified to something like:
$$ F = \frac{Gm_1m_2}{r^2} \, \exp\left(-h\int \rho(r)dr\right) $$
where $\rho(r)$ is the density of the matter. This idea is due originally to Quirino Majorana (Q. Majorana, Philos. Mag. 39 (1920) 488 - Googling finds many references to the paper but not the paper itself).
Now consider the force between two spherical masses. We can consider these masses as made up from concentric spherical shells, but the mass in each shell would shield the mass inside it. So as the masses increase and their radii increases the gravitational shielding will increase and the ratio of the shielded force to the Newtonian force will decrease. That means the ratio of the gravitational mass to the inertial mass changes as the size increases. The equivalence principle (one of its many forms) states that the ratio of gravitational to inertial mass is constant. Hence the conflict.
For the more general question of whether shielding is possible I refer to the answer from Luboš to Is it theoretically possible to shield gravitational fields or waves? The problem is that shielding generically requires a negative mass/energy and that causes all sorts of stability problems. While this isn't technically a violation of GR most of us believe that negative mass/energy cannot exist.
A: I will reply to this part of the question:

It is hard for me to believe because - suppose gravitational shielding is demonstrated somehow, then how GR can be falsified all of a sudden, which has been verified by so many experiments and phenomena. So, that makes me think gravitational shielding would not invalidate GR.

Take Newtonian gravity , which has been verified by many many experiments. When General Relativity, GR was proposed, it includes in its limiting form Newtonian gravity, and  does not invalidate it when the effect of GR is small, within measurement errors. All the results of Newtonian gravity are valid in a specific phase space of the variables, within experimental errors.
Take classical mechanics. When quantum mechanics developed for small dimensions the limits are mathematically approached smoothly as the dimensions grow large with h going to zer0.
So it is conceivable that a new gravitational theory would embed GR at the limits of some phase space. General relativity would be invalid at certain values of the variables and would need corrections but the result should join smoothly, as has happened with all validated theories of physics  when new theories are proposed to explain new phenomena.
So a theory with gravitational shielding would make sense only if it reproduces, within experimental errors , the successes in the orbits and even GPS corrections using GR, and in addition explains observations not clear using general relativity, for example dark mass and dark energy.
A: The assertion is simply wrong. The existence of negative mass by itself would not invalidate the equivalence principle, however negative mass next to a positive mass would shield $r^{-2}$ asymptotic gravitational field dependence, and only dipolar $r^{-3}$ and weaker terms would survive.
This proves you can have gravitational shielding and still preserve the equivalence principle. But it requires negative mass
