The response of museum artefacts and statues subjected to deliberate explosions of moderate intensity is investigated and their vulnerability assessed. The study focuses on the most predominant failure mechanisms, namely overturning and fracture due to the tensile stresses developed by the impact of shock waves. The rocking response is investigated relying on the existing knowledge and theory of inverted pendulum structures subjected to earthquake loading. An analytical, established approach for determining the overturning domain, developed in a previous study, is used to investigate the critical stand-off distance between the target and the explosive in order to avoid toppling. The proposed analytical model is adopted by defining appropriate correction parameters to consider the real geometry of the museum objects. We assess the overturning domain of some emblematic statues of high aesthetic and cultural value, and namely: Michelangelo's David, Farnese Hercules, Aphrodite of Milos, Athena Giustiniani, Laocoön and His Sons, and Belvedere Torso. Finally, direct damage due to the high tensile stresses is investigated and computed for different target geometries. For the dimensions and explosive quantities herein considered, overturning is found to prevail over direct material damage for targets with regular geometry.