[en] The report is concerned with potential instabilities of High-Temperature Gas-Cooled Reactor Cores supported by graphite columns. Two failure mechanisms are investigated in detail: that of torsional buckling of the entire core-column assemblage and that of column failure alone. A torsional model of the core-column assemblage is described and static buckling loads are calculated. Dynamic instability of the model to seismic loadings is also investigated. Individual column failure is examined using nonlinear graphite behavior and safety factors for static loading situations are given and compared to values given by conventional design formulas. A model of a cracked graphite column is given and buckling loads are computed for columns using a combined column and fracture mechanics analysis. A finite element analysis of a cracked graphite column is presented