The modern radiation technology, nuclear engineering, non-linear optics are associated with radiation-resistant optical material study. Evolution of electronic excitations in these materials is a complex multichannel process which currently has no integrated model. A special role belongs to the low-symmetry single crystals, such as beryllium oxide (BeO). We present theoretical results that advance our understanding of exciton-based channel of electronic excitations relaxation. The four possible self-trapped exciton (STE) configurations in beryllia single crystal have been investigated by using a quantum mechanical approach (Hartree-Fock and B3LYP HF-DFT hybrid functional, as implemented in the CRYSTAL09 code). B3LYP DFT functional with 30% of exact exchange was used (B3LYP30). All calculations were performed using periodic boundary conditions and full SC geometry relaxation. The lattice distortion and charge density distribution for considered defect configurations were obtained. STE-A1 luminescence energy was found to be 6.0 eV for HF and 6.5 eV for B3LYP30; STE-A2 luminescence energy was found to be 9.2 eV for HF and 7.8 eV for B3LYP30. STE-B1 luminescence energy was found to be 5.5 eV for HF, 6.2 eV for B3LYP30; STE-B2 luminescence energy was found to be 4.7 eV for HF.