A theoretical modelling of the oxygen diffusivity in silicon, germanium and Si1-xGex (O) crystals both at normal and high hydrostatic pressure has been carried out using molecular mechanics, semiempirical and ab initio methods. It was established that the diffusion process of an interstitial oxygen atom (Oi) is controlled by the optimum configuration of three silicon (germanium) atoms nearest to Oi. The calculated values of the activation energy Ea (Si) = 2.59 eV, Ea(Ge) = 2.05 eV and pre-exponential factor D0(Si) = 0.28 cm2 s−1, D0(Ge) = 0.39 cm2 s−1 are in good agreement with experimental ones and for the first time describe perfectly the experimental temperature dependence of the Oi diffusion constant in Si crystals (T = 350–1200 °C). Hydrostatic pressure (P ≤ 80 kbar) results in a linear decrease of the diffusion barrier (∂P Ea (P) = −4.38 × 10−3 eV kbar−1 for Si crystals). The calculated pressure dependence of Oi diffusivity in silicon crystals agrees well with the pressure-enhanced initial growth of oxygen-related thermal donors. The simulation (PM5) has revealed that in Si1-xGex crystals there are two mechanisms of variation of Oi diffusion barrier. The increase of lattice constant leads to the linear increase of the diffusion barrier. Strains around Ge atoms decrease the diffusion barrier. Formation of gradient of diffusion barrier in the volume of Si1-xGex may be responsible for the experimentally observed suppression of generation of TD in Si1-xGex (O) crystals.