The response of monumental buildings to internal explosions is here investigated through a numerical approach. The study focuses on the emblematic case of the Pantheon in Rome, yet it sheds light on more generic ones. Propagation of incident and reflected blast waves and their impact on the structure are considered in terms of a coupled solid-fluid simulation which relies on a multi-material formulation. The pre-existent cracks spreading the dome and the material non-linearities of low-tensile strength concrete aggregates are considered. The geometry of the structure is accounted by a detailed three-dimensional model. The numerical results draw a picture where the use of empirical laws to model blast actions in structures with complex geometry may be inadequate. In fact, the coupled solid-fluid simulations show strong localizations of shock waves due to the dome-vaulted geometry which concentrates the energy released by the explosion as a concave mirror. The structural response is highly influenced by the high-pressure volume which stems from wave localization phenomena in the centre of the dome as well as by the presence of the pre-existent cracks.