Electron stimulated desorption (ESD) of neutral atomic Cs from graphene on Ir has been studied for two cases: when Cs intercalation does present and when it does not take place. Two peaks have been found at desorbed atom energy distribution: high-energy (HE) at the energy of 0.36 eV and low-energy (LE) one at the energy of 0.13 eV. HE peak has been observed for both cases, we attribute it with excitation of 2s carbon core level. LE peak was observed only when intercalation does not take place; we attribute it with excitation of 4f and 5p core levels of Ir. A model is put forward to describe atomic Cs ESD; we proposed that graphene on Ir acts as dielectric in the processes discussed above.