  The variation of the superconducting critical temperature Tc as a function of
the pressure p in the magnesium diboride MgB2 has been studied in the framework
of two-bands Eliashberg theory and traditional phonon coupling mechanism. I
have solved the two-bands Eliashberg equations using first-principle
calculations or simple assumptions for the variation, with the pressure, of the
relevant physical quantities. I have found that the experimental Tc versus p
curve can be fitted very well and information can be obtained on the dependence
of the electron-phonon interaction matrix <I^{2}> by pressure. The pressure
dependence of the superconductive gaps Delta{sigma} and Delta{pi} is also
predicted.
