It is proposed to use X-ray radiation of remote radio galaxies resulti
ng from Compton scattering of photons of the 3K-background radiation b
y relativistic gas in extended components of radio galaxies in order t
o experimentally determine the geometry of the Universe. For 32 object
s (photometric red shifts of most of them exceed unity) detected with
RATAN-600 their expected X-ray radiation was estimated for all major m
odels of the Universe. It is shown that large remote radio galaxies of
this list can be observed even with existing X-ray telescopes.