We evaluated the buckling limit of a conceptually designed reactor vessel of the Advanced Burner Test Reactor (ABTR) for a horizontal safe shutdown earthquake (SSE) seismic load. In this evaluation, both seismic isolation and non-isolation designs were considered for thin reactor vessels subjected to elevated temperature services. For calculating the buckling load, two kinds of methods, a numerical simulation method using finite element analysis and an evaluation formula driven from a theoretical basis, were used. To consider the material aging effect caused by a 60-year design lifetime and $510^{circ}C$ normal operating temperature, an isochronous stress-strain curve corresponding to these conditions was used for the nonlinear elastic-plastic buckling analysis method. From the evaluation results of the buckling load, it was found that plasticity behavior significantly affects the buckling strength, but that the initial geometrical imperfections have little effect. Also, the non-seismic isolation design does not satisfy the buckling limit rules of the ASME BPV Section III, Subsection NH, but the seismic isolation design does satisfy it with sufficient margins.