We investigate dynamic buckling of aboveground steel tanks with conical roofs and anchored to the foundation, subjected to horizontal components of real earthquake records. The study attempts to estimate the critical horizontal peak ground acceleration (Critical PGA), which induces elastic buckling at the top of the cylindrical shell, for the impulsive hydrodynamic response of the tank–liquid system. Finite elements models of three cone roof tanks with height to diameter ratios (H/D) of 0.40, 0.63 and 0.95 and with a liquid level of 90% of the height of the cylinder were used in this study. The tank models were subjected to accelerograms recorded during the 1986 El Salvador and 1966 Parkfield earthquakes, and dynamic buckling computations (including material and geometric non-linearity) were carried out using the finite element package ABAQUS. For the El Salvador accelerogram, the critical PGA for buckling at the top of the cylindrical shell decreased with the H/D ratio of the tank, while similar critical PGAs regardless of the H/D ratio were obtained for the tanks subjected to the Parkfield accelerogram. The elastic buckling at the top occurred as a critical state for the medium height and tallest models regardless of the accelerogram considered, because plasticity was reached for a PGA larger than the critical PGA. For the shortest model (H/D = 0.40), depending on the accelerogram considered, plasticity was reached at the shell before buckling at the top of the shell.