We investigate the dynamics of inverted pendulum structures under fast-dynamic excitations arising from an explosion. We model blast actions using established empirical models and best-fit interpolations of existing experimental tests. We focus attention on pure rocking response mechanisms. We present moment balance equations and overturning conditions. Inspired by previous works in the frame of earthquake engineering, we derive new analytical, closed-form solutions for the rocking response and the overturning domain of slender blocks due to explosions. The analytical findings and assumptions are validated through existing experimental tests and detailed three-dimensional numerical simulations, which consider the full interaction between the blast waves and the structure. We show that unilateral rocking response and overturning are predominant mechanisms compared to sliding and up-lifting. Finally, we develop design charts to be used as a straightforward decision making tool for determining the critical stand-off distance between the explosive source and the target in order to prevent overturning. Our model can be easily applied for the design of protective devices to preserve artefacts, secure buildings and humans, as well as for devising energy absorbing systems based on rocking.