By using the wavefunctions obtained from diagonalizing the complete ds energy matrix at normal and various pressures,the g factor of the ground state of SrTiO3 :Cr3+ and its pressure-induced shift have been microscopically calculated.Only by taking the local strains around Cr3+ in SrTiO3:Cr3+ (which are about twice the bulk ones) and corresponding P-χ dependence,can we obtain a good agreement between the calculated result of pressure-induced shift of ground-state g factor and the experimental one.The physical origins of this pressure-induced shift have been explained.It is found that the change of Dq-1 with pressure makes main contribution to the pressure-induced shift of ground-state g factor of SrTiO3 :Cr3+.By using the wavefunctions obtained from diagonalizing the complete d3 energy matrix at normal pressure,the relevant matrix elements and accordingly strain-induced splittings of t32 2E and t23 4A2 of SrTiO3:Cr3+ have been calculated.The important results of Yc,Zc,Pc and Qc have also been evaluated.It is the admixtures of basic wavefunctions resulted from the spin-orbit interaction and/or Coulomb interaction and/or Kramers degeneracy that make the strain-induced splittings of the levels nonzero.It is found that there are nonvanishing matrix elements of operators T2,T2rl and T2 between wavefunctions with positive Ms and those with negative M],which have important effects on the strain-induced splittings of the levels.