  The Lorentz invariant formalism for description of neutrino flavour
oscillations in moving matter is developed. It is shown that the matter motion
with relativistic speed can sufficiently change the matter term in the neutrino
effective potential. In the case of matter motion parallel to neutrino
propagation, matter effects in neutrino flavour oscillations are suppressed. In
the case of relativistic motion of matter in the opposite direction in respect
to neutrino propagation, sufficient increase of effects of matter in neutrino
oscillations is predicted. The effective neutrino flavour oscillation
probability, effective mixing angle and oscillation length, as well as the MSW
effect resonance condition for the case of moving matter are derived.
