[en] The classical model of an ideal crystal parameterized with the ab initio data is applied to determine the structure, geometry and thermodynamic stability of the trapping sites of atomic lithium in solid rare gases RG = Ar, Kr and Xe. The variety of the stable sites found is represented by the four highly symmetric structures that correspond to the octahedral interstitial occupation, single substitution and accommodations of Li atom in the tetrahedral and octahedral vacancies formed by removal of four and six RG atoms from the lattice, respectively. The distance-dependent isotropic component of the hyperfine interaction tensor calculated ab initio for the Li–RG diatomic complexes are used to estimate the shifts of the electron paramagnetic resonance signals for predicted stable trapping sites. Comparison with the literature data allows for consistent assignment of the multiple observed EPR signals to the stable trapping sites of the certain types, which accounts for the variations in the spectra of samples with thermal deposition or laser ablation of Li in the different rare gas matrices. (author)