The rare gas (Ne, Ar, Kr, Xe)-alkali metal (Li, Na) ground-state pair interaction potentials and distance-dependent isotropic hyperfine coupling constants are evaluated by coupled-cluster approaches at the van der Waals region of the dimers. The computed properties are further utilized in classical molecular dynamics simulations of rare gas lattices doped with alkali atoms. Atomic trajectories and time averaged hyperfine constants are obtained from the simulations and exploited to provide theoretical insights into experimentally observed atomic trapping and dynamics of alkali metal atoms in rare gas matrices. The simulations support our previous electron paramagnetic resonance (EPR) data [Chem. Phys. Lett, 310, 245 (1999)], suggesting that alkali metal atoms, while generated by laser vaporization, do trap in single substitutional sites, whereas thermal atom sources yield trapping in multiple substitutional sites. In order to theoretically reproduce the EPR spectra for the latter case, more than six neighboring vacancies had to be included in the model system. Based on the simulations, the trapped atoms are able to move rather freely within the extended cage.