Cosmic-rays are subatomic particles of energies ranging between a few eV to hundreds of TeV. These particles register a power-law spectrum, and it seems that most of them originate from astrophysical galactic and extragalactic sources. The shock acceleration in superalfvenic astrophysical plasmas, is believed to be the main mechanism responsible for the production of the non-thermal cosmic-rays. Especially, the importance of the very high energy cosmic-ray acceleration, with its consequent gamma-ray radiation and neutrino production in the shocks of the relativistic jets of Gamma Ray Bursts, is a favourable theme of study. I will discuss the cosmic-ray shock acceleration ...