The complete active space (GAS) configuration interaction (CI) and CASSCF calculations for naked Cr(II)-Cr(II) (1) and Mo(II)-Mo(II) (2) dimers were carried out in order to examine the reliability of the previous MO-theoretical results obtained by the ab initio UHF and DFT methods. From the CASCI and CASSCF calculations, it was concluded that the formal bond orders (one sigma, two pi, and one delta bonds) are reduced to the effective ones due to the strong correlation and also that the valence-bond (VB) like model such as the Heisenberg model works well in 1. The effective exchange integrals (J(ab)) calculated for the system were compatible with the experimental results available. On the other hand, the sigma and pi bonds in 2 were strong, showing that the MO picture is reliable. The delta bond of 2 was calculated to be rather weak, although it is stronger than that of 1. The CASCI and CASSCF results support the previous UHF and DFT results for 1 and 2.