In this paper we present the results of an ab initio model potential (AIMP) embedded-cluster study of the ground and lowest excited states of Cr3+ defects in the elpasolites Cs2NaYCl6 and Cs2NaYBr6; complete active space SCF (CASSCF) and averaged coupled-pair functional (ACPF) calculations are performed on CrCl63- and CrBr63- clusters embedded in ab initio model potential representations of the surrounding lattices Cs2NaYCl6 and Cs2NaYBr6. The experimental structural data are revisited and some new results are found which differ significantly from those available in the literature. The calculated local structure parameters and electronic transition energies which can be compared to experiments are found to be very good; new structural and spectroscopic results are produced which have been neither measured nor calculated, which are complementary to the available ones, and whose quality is expected to be high as well. In particular, the question of the competition of the excited-state absorptions with the potential vibronic laser emission has been adressed: A considerable overlap between the broad E-2(g) --> (2)A(1g) excited-state absorption and (4)A(2g) <-- T-4(2g) emission bands is predicted in both materials, which must result in a reduction in the emission efficiency. Finally, it is shown that the quantum mechanical embedding effects due to the fact that the external Cs+, Na+, Y3+, Cl-, and Br- ions are not point charges, are non-negligible; lacking of these effects must be one of the reasons which make previous Density Functional Theory calculations show significantly larger discrepancies with the available experiments.