Graphite materials are used for structural components in the core of high temperature gas-cooled reactors (HTGRs) because of their excellent thermo/mechanical properties. When the core temperature is raised at an accident, the thermal stress of the components is induced, and it enhances the fracture probability of them. In general, the thermal conductivity of graphite is decreased by neutron irradiation due to irradiation-induced defects preventing heat conduction by phonon. It is hence expected that decreased thermal conductivity is recovered to some extent by thermal annealing at the accident. Therefore, the consideration of the thermal annealing effect is placed as much important subject in the fracture/strength evaluation of the graphite components at the accident. In the present study, the thermal stress and the fracture probability of graphite components influenced by the thermal annealing were investigated by a finite element method (FEM) analysis. It was shown that the annealing effect decreases the thermal stress and a certain level of the fracture probability.