The potential energy surfaces of atomic oxygen, O(3P, 1D, 1S), trapped in crystalline Kr and Xe are developed based on known angularly anisotropic pair interactions. The electrostatic limit, with the neglect of exchange and spin-orbit interactions, is assumed. Using a classical statistical treatment for the simulation of spectra, the surfaces are shown to reproduce the experimental O(1S-->1D) emissions in substitutional and interstitial sites of crystalline Kr. The surfaces are also in accord with charge transfer emission spectra of O/Xe solids. With lattice relaxation, the Xe-O(1D)-Xe insertion site becomes the global minimum, and can therefore act as a stable trap site. This is in accord with experimental observations of a third trapping site in Xe. To rationalize the recently reported long-range mobility of O atoms in these solids [A. V. Danilychev and V. A. Apkarian, J. Chem. Phys. 99, 8617 (1993)], the topology of various electronic surfaces are presented. It is shown that the minimum energy paths connecting interstices on the triplet and singlet surfaces are quite different. The triplet path is strongly modulated and proceeds along body diagonals of the unit cell. The singlet path is more gently modulated and proceeds along face diagonals. These features are consistent with the postulated thermal mobility as proceeding via triplet-singlet conversion. However, on a quantitative basis, the electrostatic surfaces fail to support the model. The site specific crossing energies, including lattice relaxation, are calculated to range between 1.2 and 1.7 eV in Xe and Kr, which is an order of magnitude larger than the observed experimental activation energies of migration. Inclusion of spin-orbit and charge transfer mixing in these surfaces, absent in the present treatment, should reduce this discrepancy.